OFFSET
1,1
COMMENTS
Numbers k whose sum of aliquot divisors that are abundant numbers is > k.
If k is a term then all the positive multiples of k are also terms.
The smallest odd term is a(10042) = 155925.
The numbers of terms not exceeding 10^k for k = 1, 2, ... are 0, 2, 53, 629, 6423, 63932, 639947, 6395539, 63934596, ... Apparently, this sequence has an asymptotic density 0.0639...
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
EXAMPLE
The divisors of 60 are {1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60}. The abundant divisors are {12, 20, 30, 60} and their sum is 122 > 2*60 = 120. Therefore, 60 is a term.
MATHEMATICA
abQ[n_] := DivisorSigma[1, n] > 2*n; s[n_] := DivisorSum[n, # &, abQ[#] &]; q[n_] := s[n] > 2*n; Select[Range[1000], q]
PROG
(PARI) isok(k) = 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