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A115414 Odd abundant numbers not divisible by 3. 4
5391411025, 26957055125, 28816162375, 33426748355, 34393484125, 37739877175, 40342627325, 48150877775, 50866790975, 53356378075, 55959128225, 59305521275, 60711976325, 61164628525, 63395557225, 64899009175, 67275433225, 68972878975, 70088343325, 74922022175, 75665665075 (list; graph; refs; listen; history; text; internal format)
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_i-1/p_i^e_i)/(p_i-1) < 1/2 Product p_i/(p_i-1). See A064001 for odd abundant numbers not divisible by 5.- M. F. Hasler, Jul 27 2016

LINKS

Donovan Johnson, Table of n, a(n) for n = 1..394 (terms < 10^12)

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: A017409 A017529 A133688 * 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

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Last modified March 27 02:45 EDT 2017. Contains 284144 sequences.