A348605 Odd nonexponential abundant numbers: odd numbers k such that A160135(k) > k.

8505, 10395, 12285, 15015, 16065, 17955, 19635, 21735, 21945, 23205, 25515, 25935, 26565, 28875, 31185, 31395, 33495, 33915, 34125, 35805, 36855, 39585, 41055, 42315, 42735, 45885, 47355, 48195, 49665, 50505, 51765, 53865, 54285, 55965, 56595, 58695, 61215, 64155

Offset: 1

Author

Amiram Eldar, Oct 25 2021

Keywords

• nonn

Comments

The odd terms of A348604.

The numbers of terms not exceeding 10^k, for k = 4, 5, ..., are 1, 51, 360, 4117, 39803, 418663, 4099004, ... Apparently this sequence has an asymptotic density 0.0004...

Examples

			8505 is a term since A160135(8505) = 8862 > 8505.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A160135.

Subsequence of A005231 and A348604.

Similar sequences: A094889, A127666, A129485, A293186, A321147, A348275.

Programs

Mathematica

esigma[n_] := Times @@ (Sum[First[#]^d, {d, Divisors[Last[#]]}] &) /@ FactorInteger[n]; q[n_] := DivisorSigma[1, n] - esigma[n] > n; Select[Range[1, 65000, 2], q]