OFFSET
1,1
COMMENTS
Obviously A337346(n) = 0 for any noncomposite and for any semiprime, thus this is a subsequence of A033942. The first term of A033942 not present here is 125, as A337345(125) = 1.
Empirically checked: in range 1 .. 2^31, all abundant numbers are found in this sequence. For proving this, we should concentrate only on checking A091191, as the set A005101 \ A091191 (non-primitive abundant numbers) is certainly included, as for any divisor d for which sigma(d) > 2*d (or even sigma(d) >= 2*d), we also have A003961(d) > 2*d.
LINKS
MATHEMATICA
Block[{nn = 165, s}, s = {1}~Join~Array[Times @@ Map[#1^#2 & @@ # &, FactorInteger[#] /. {p_, e_} /; e > 0 :> {Prime[PrimePi@ p + 1], e}] &, nn - 1, 2]; Select[Range[nn], 1 < DivisorSum[#, 1 &, s[[#]] > 2 # &] &]] (* Michael De Vlieger, Feb 22 2021 *)
PROG
CROSSREFS
KEYWORD
nonn
AUTHOR
Antti Karttunen, Feb 22 2021
STATUS
approved