

A115414


Odd abundant numbers not divisible by 3.


6



5391411025, 26957055125, 28816162375, 33426748355, 34393484125, 37739877175, 40342627325, 48150877775, 50866790975, 53356378075, 55959128225, 59305521275, 60711976325, 61164628525, 63395557225, 64899009175, 67275433225, 68972878975, 70088343325, 74922022175, 75665665075
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OFFSET

1,1


COMMENTS

An odd abundant number (A005231) not divisible by 3 must have at least 7 distinct prime factors (e.g., 5^4*7^2*11^2*13*17*19*23) and be >= 5*29#/3# = 5^2*7*11*13*17*19*23*29 = 5391411025 = A047802(2) = a(1). This is most easily seen by writing the relative abundancy A(N) = sigma(N)/2N = sigma[1](N) as A(Product p_i^e_i) = 1/2 Product (p_i1/p_i^e_i)/(p_i1) < 1/2 Product p_i/(p_i1). See A064001 for odd abundant numbers not divisible by 5. M. F. Hasler, Jul 27 2016


LINKS

Giovanni Resta, Table of n, a(n) for n = 1..4343 (terms < 10^13, first 394 terms from Donovan Johnson)
Eric Weisstein's World of Mathematics, Abundant Number


EXAMPLE

a(1)=5391411025 because it is the smallest abundant number (sigma(n)/n =~ 2.003) that is not divisible by 2 or 3.


PROG

(PARI) is(n)=gcd(n, 6)==1 && sigma(n, 2)>2 \\ Charles R Greathouse IV, Jul 28 2016


CROSSREFS

Cf. A005101, A005231, A064001, A112640, A112644.
Sequence in context: A335084 A133688 A306497 * A112430 A272714 A213254
Adjacent sequences: A115411 A115412 A115413 * A115415 A115416 A115417


KEYWORD

nonn


AUTHOR

Sergio Pimentel, Mar 08 2006


EXTENSIONS

Added missing term 55959128225 and a(14)a(16) from Donovan Johnson, Dec 29 2008
a(17)a(20) from Donovan Johnson, Dec 01 2011
More terms from M. F. Hasler, Jul 28 2016


STATUS

approved



