A047802 - OEIS

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A047802

Smallest abundant number (sigma(x) > 2x) which is not divisible by any of the first n primes.

12, 945, 5391411025, 20169691981106018776756331, 49061132957714428902152118459264865645885092682687973, 7970466327524571538225709545434506255970026969710012787303278390616918473506860039424701 (list; graph; refs; listen; history; text; internal format)

	OFFSET	`0,1`
	COMMENTS	`a(n) exists for every n, since the sum of the inverses of the primes is infinite.` `Heuristic: square the first several primes and then add successive primes until the number is abundant. - Fred Schneider (frederick.william.schneider(AT)gmail.com), Sep 20 2006` `For terms 3 4 and 5, squaring only the first two will be part of the minimal solution: 49061132957714428902152118459264865645885092682687973 = 11^2 * 13^2 * 17 * 19 * 23 * 29 * 31 * 37 * 41 * 43 * 47 * 53 * 59 * 61 * 67 * 71 * 73 * 79 * 83 * 89 * 97 * 101 * 103 * 107 * 109 * 113 * 127 * 131 * 137 - Fred Schneider (frederick.william.schneider(AT)gmail.com), Sep 20 2006` `a(5) = 13^2 * 17^2 * 19 * 23 * ... * 223 * 227 - Fred Schneider (frederick.william.schneider(AT)gmail.com), Sep 20 2006` `a(6) = 17^2 * 19^2 * 23^2 * 29 * 31 * ... * 347 * 349 and` `a(7) = 19^2 * 23^2 * 29^2 * 31 * 37 * ... * 491 * 499 (both coming from D. Iannucci paper). Michel Marcus, May 01 2013`
	REFERENCES	`M. T. Whalen and C. L. Miller, Odd abundant numbers: some interesting observations, Journal of Recreational Mathematics 22 (1990), pp. 257-261.`
	LINKS	`Table of n, a(n) for n=0..5.` `Douglas Iannucci, On the smallest abundant number not divisible by the first k primes, Bulletin of the Belgian Mathematical Society 12:1 (2005), pp. 39-44.`
	FORMULA	`Iannucci shows that log a(n) = (n log n)^(2 + o(1)).`
	EXAMPLE	`a(0) = 12, the first abundant number; a(1) = 945, the first odd abundant number; a(5) is the first abundant number not divisible by 2,3,5,7 or 11.`
	CROSSREFS	`Subsequence of A005101 and A133812; c.f. A005231.` `Sequence in context: A203599 A114809 A114371 * A180237 A079916 A204327` `Adjacent sequences: A047799 A047800 A047801 * A047803 A047804 A047805`
	KEYWORD	`nonn,changed`
	AUTHOR	`Ulrich Schimke (ulrschimke(AT)aol.com)`
	EXTENSIONS	`2 more terms from Fred Schneider (frederick.william.schneider(AT)gmail.com), Sep 20 2006` `Reference by Charles R Greathouse IV, Dec 07 2009` `Reference and formula from Charles R Greathouse IV, Feb 16 2011`
	STATUS	`approved`

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Last modified May 22 00:00 EDT 2013. Contains 225507 sequences.