A348604 Nonexponential abundant numbers: numbers k such that A160135(k) > k.

24, 30, 42, 48, 54, 60, 66, 70, 72, 78, 84, 90, 96, 102, 114, 120, 126, 132, 138, 150, 156, 160, 162, 168, 174, 180, 186, 192, 198, 210, 216, 222, 224, 240, 246, 258, 264, 270, 280, 282, 288, 294, 300, 312, 318, 320, 330, 336, 352, 354, 360, 366, 378, 384, 390

Offset: 1

Author

Amiram Eldar, Oct 25 2021

Keywords

• nonn

Comments

The smallest odd term is a(1357) = 8505.

The numbers of terms not exceeding 10^k, for k = 1, 2, ..., are 0, 13, 148, 1595, 15688, 158068, 1578957, 15762209, 157745113, 1577808429, ... Apparently this sequence has an asymptotic density 0.157...

Examples

			24 is a term since A160135(24) = 30 > 24.
		

Links

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

Crossrefs

Cf. A160135, A348601.

Subsequence of A005101.

Similar sequences: A034683, A064597, A129575, A129656, A292982, A348274.

Programs

Mathematica

esigma[n_] := Times @@ (Sum[First[#]^d, {d, Divisors[Last[#]]}] &) /@ FactorInteger[n]; q[n_] := DivisorSigma[1, n] - esigma[n] > n; Select[Range[400], q]