OFFSET
1,1
COMMENTS
Only composite numbers are considered because if p is prime then the sigma(p) = p + 1 is divided by 1' + p' = 0 + 1 = 1 and sigma(p) is divisible of 1.
EXAMPLE
MATHEMATICA
d[0] = d[1] = 0; d[n_] := n * Plus @@ ((Last[#]/First[#]) & /@ FactorInteger[n]); s[n_] := DivisorSum[n, d[#] &]; Select[Range[10000], CompositeQ[#] && Divisible[DivisorSigma[1, #], s[#]] &] (* Amiram Eldar, Oct 18 2021 *)
PROG
(Magma) f:=func<n |n le 1 select 0 else n*(&+[Factorisation(n)[i][2]/Factorisation(n)[i][1]: i in [1..#Factorisation(n)]])>; [k:k in [2..10300]|not IsPrime(k) and DivisorSigma(1, k) mod &+[Floor(f(d)): d in Divisors(k)|d ne 1] eq 0];
(PARI) ad(n) = if (n<1, 0, my(f = factor(n)); n*sum(k=1, #f~, f[k, 2]/f[k, 1])); \\ A003415
isok(k) = (k>1) && !isprime(k) && !(sigma(k) % sumdiv(k, d, ad(d))); \\ Michel Marcus, Oct 19 2021
CROSSREFS
KEYWORD
nonn
AUTHOR
Marius A. Burtea, Oct 18 2021
STATUS
approved