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
This is not a subsequence of A248150. For example, 81324229811825 and 37182145^2 = 1382511906801025 are terms, with sigma(.) == 2 (mod 4) and sigma(.) == 3 (mod 4) respectively. - Amiram Eldar, Aug 24 2020
LINKS
David A. Corneth, Table of n, a(n) for n = 1..42320 (terms < 10^14, terms 1..394 from Donovan Johnson, terms 395..4343 from Giovanni Resta)
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, -1)>2 \\ Charles R Greathouse IV, Jul 28 2016
CROSSREFS
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