A348630 Nonexponential superabundant numbers: numbers m such that nesigma(m)/m > nesigma(k)/k for all k < m, where nesigma(m) is the sum of nonexponential divisors of m (A160135).

1, 24, 30, 96, 120, 480, 840, 3360, 13440, 30240, 36960, 120960, 147840, 272160, 332640, 1330560, 2993760, 4324320, 17297280, 38918880, 73513440, 220540320, 294053760, 661620960, 1396755360, 2646483840, 5587021440, 12570798240

Offset

1,2

Comments

The least term k with nesigma(k)/k > m for m = 2, 3, 4, ... is 480, 332640, 1396755360, ...

Links

Table of n, a(n) for n=1..28.

Mathematica

esigma[n_] := Times @@ (Sum[First[#]^d, {d, Divisors[Last[#]]}] &) /@ FactorInteger[n]; s[1] = 1 ; s[n_] := DivisorSigma[1, n] - esigma[n]; seq = {}; rm = -1; Do[r1 = s[n]/n; If[r1 > rm, rm = r1; AppendTo[seq, n]], {n, 1, 10^6}]; seq

Crossrefs

Cf. A160135, A348604.

Subsequence of A348629.

The nonexponential version of A004394.

Similar sequences: A002110 (unitary), A037992 (infinitary), A061742, A292984, A329882, A348273.

Sequence in context: A135045 A109321 A349689 * A067952 A239801 A123200

Adjacent sequences: A348627 A348628 A348629 * A348631 A348632 A348633

Keyword

nonn,more

Author

Amiram Eldar, Oct 26 2021

Status

approved