A348273 Noninfinitary superabundant numbers: numbers m such that nisigma(m)/m > nisigma(k)/k for all k < m, where nisigma(m) is the sum of noninfinitary divisors of m (A348271).

1, 4, 12, 16, 36, 48, 144, 720, 3600, 25200, 176400, 226800, 1587600, 1940400, 2494800, 17463600, 32432400, 192099600, 227026800, 2497294800, 3632428800, 32464832400, 39956716800

Offset: 1

Author

Amiram Eldar, Oct 09 2021

Keywords

• nonn
• more

Comments

The least term k with A348271(k)/k > m for m = 1, 2, 3, .... is 36, 3600, 1587600, ...

Crossrefs

Cf. A348271.

Subsequence of A348272.

The noninfinitary version of A004394.

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

Programs

Mathematica

f[p_, e_] := Module[{b = IntegerDigits[e, 2], m}, m = Length[b]; Product[If[b[[j]] > 0, 1 + p^(2^(m - j)), 1], {j, 1, m}]]; isigma[1] = 1; isigma[n_] := Times @@ f @@@ FactorInteger[n]; s[n_] := DivisorSigma[1,n] - isigma[n]; seq = {}; rm = -1; Do[r1 = s[n]/n; If[r1 > rm, rm = r1; AppendTo[seq, n]],{n, 1, 10^6}]; seq