A348273 - OEIS

%I #5 Oct 12 2021 14:01:08

%S 1,4,12,16,36,48,144,720,3600,25200,176400,226800,1587600,1940400,

%T 2494800,17463600,32432400,192099600,227026800,2497294800,3632428800,

%U 32464832400,39956716800

%N 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).

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

%t 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

%Y Cf. A348271.

%Y Subsequence of A348272.

%Y The noninfinitary version of A004394.

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

%K nonn,more

%O 1,2

%A _Amiram Eldar_, Oct 09 2021