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Topic: Noncototient

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	Noncototient - Wikipedia, the free encyclopedia
		A noncototient is a positive integer n that can not be expressed as the difference between a positive integer m and the number of coprime integers below it.
		The cototient of n is defined as n-φ(n), so a noncototient is a number that is never a cototient.
		It is conjectured that all noncototients are even.
	en.wikipedia.org /wiki/Noncototient (306 words)

	Talk:Noncototient - Wikipedia, the free encyclopedia
		But until someone can say for sure which density is referred to and explain it to the others, I've decided to take Primefan's advise and remove the statement.
		A paper of Banks and Luca at Arxiv math.NT/0409231 shows that the number of noncototients less than X is bounded below by (1/2 + o(1))X/log X [which might well be added to the article --- the Flammenkamp--Luca result gives only a constant multiple of log X as lower bound].
		The natural question is thus to ask whether the set of noncototients has positive lower density in the asymptotic sense: that is, whether there is a constant c>0 such that the number of noncototients less than X is infinitely often greater than cX.
	en.wikipedia.org /wiki/Talk:Noncototient (337 words)

	50 (number) - Wikipedia, the free encyclopedia (Site not responding. Last check: 2007-10-23)
		There is no answer to the equation φ(x) = 50, making 50 a nontotient.
		Nor is there an answer to the equation x - φ(x) = 50, making 50 a noncototient.
		The traditional number of years in a default jubilee period.
	www.encyclopedia-online.info /Fifty (270 words)

	Noncototient - Free net encyclopedia (Site not responding. Last check: 2007-10-23)
		This follows from a modified form of the Goldbach conjecture: if the even number n can be represented as a sum of two distinct primes p and q, then
		It is expected that every even number larger than 6 is a sum of distinct primes, so probably no odd number larger than 5 is a noncototient.
		This was finally answered in the affirmative by Browkin and Schinzel (1995), who showed every member of the infinite family $2^k \cdot 509203$ is an example.
	www.netipedia.com /index.php/Noncototient (283 words)

	10 (number)
		But it is also a triangular number and a centered triangular number.
		Ten is the smallest noncototient, a number that can not be expressed as the difference between any integer and the total of coprimes below it.
		Ten is a Harshad number and a semi-meandric number.
	www.askfactmaster.com /10_(number) (537 words)

	Certificate dollar silver ten (Site not responding. Last check: 2007-10-23)
		Givens official acts of noncototient, a certificate dollar silver ten portion before he had.
		Pac-10 and ms thesis rush, i prefer the youre all downward.
		Noncototient, a certificate dollar silver ten of miriam which communicate ez introduction.
	ten.poleham.com /certificate-dollar-silver-ten.php (188 words)

	Quaest.io on 200 Number (Site not responding. Last check: 2007-10-23)
		Also, the title of the Star Trek: The Next Generation episode "11001001", also the area code for northwestern New Jersey.
		Two hundred three 203 = 7·29, 6th Bell number, also HTTP status code indicating partial information, also the area code for Southwest Connecticut - Fairfield and New Haven counties.
		The continued fraction representation of pi is [3; 7, 15, 1, 292, 1, 1, 1, 2...]; the convergent obtained by truncating before the surprisingly large term 292 yields the excellent rational approximation 355/113 to pi.
	www.quaest.io /?title=200-number (1661 words)

	58 (number)
		Fifty-eight is the sum of the first seven prime numbers, an 11-gonal number, and a Smith number.
		There is no answer to the equation x - φ(x) = 50, making 50 a noncototient.
		The code for international direct dial phone calls to Venezuela.
	www.askfactmaster.com /58_(number) (109 words)

	300 (number) (Site not responding. Last check: 2007-10-23)
		Several varieties of calendar have resulted from attempts to divide the 29.5-day lunar month and traditional 7-day week into the 365.25 day year.
		Three hundred seventy one CCCLXXI 371 = 7·53, sum of three consecutive primes (113 + 127 + 131), sum of seven consecutive primes (41 + 43 + 47 + 53 + 59 + 61 + 67)
		Three hundred eighty six CCCLXXXVI 386 = 2·193, noncototient, also shorthand for the Intel 80386 microprocessor chip
	www.aseannewsnetwork.de /articles/content/3/30/300__number_.html (1782 words)

	www.myspace.com/ccxxii
		It is a repdigit composite number, and its factorization makes it a sphenic number.
		There is no solution to the equation x - f(x) = 222, making 222 a noncototient.
		Nor is there, in base 10, an integer that added to the sum of its own digits yields 222, making 222 a self number.
	www.myspace.com /ccxxii (840 words)

	The world's top 200 number websites (Site not responding. Last check: 2007-10-23)
		Two hundred six 206 = 2·103, nontotient, noncototient, also the area code for Seattle, Washington.
		Two hundred sixty-six 266 = 2·7·19, sphenic number, Harshad number, nontotient, noncototient
		Two hundred ninety 290 = 2·5·29, sphenic number, sum of four consecutive primes (67 + 71 + 73 + 79), nontotient, noncototient
	www.websbiggest.com /wiki-article-tab.cfm/200__number_ (1342 words)

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