OFFSET
1,1
COMMENTS
The numbers of terms not exceeding 10^k for k = 6, 7, ... are 25, 352, 3281, 33291, 336686, ... Apparently, this sequence has an asymptotic density 0.000033...
Apparently, the least term that is not divisible by 3 is 836504377583875.
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
EXAMPLE
The divisors of 155925 that are abundant numbers are {945, 1575, 2835, 3465, 4725, 5775, 7425, 10395, 14175, 17325, 22275, 31185, 51975, 155925}. Their sum is 330000 > 2*155925 = 311850. Therefore, 155925 is a term.
MATHEMATICA
abQ[n_] := DivisorSigma[1, n] > 2*n; s[n_] := DivisorSum[n, # &, abQ[#] &]; q[n_] := s[n] > 2*n; Select[Range[1, 1000000, 2], q]
PROG
(PARI) isok(k) = (k%2) && sumdiv(k, d, if (sigma(d)>=2*d, d)) > 2*k; \\ Michel Marcus, Sep 20 2021
CROSSREFS
KEYWORD
nonn
AUTHOR
Amiram Eldar, Sep 20 2021
STATUS
approved