A348272 Noninfinitary highly abundant numbers: numbers m such that nisigma(m) > nisigma(k) for all k < m, where nisigma(k) is the sum of noninfinitary divisors of n (A348271).

1, 4, 9, 12, 16, 28, 36, 48, 80, 100, 112, 144, 180, 240, 300, 324, 336, 396, 400, 432, 468, 528, 576, 684, 720, 900, 1008, 1200, 1296, 1584, 1872, 2160, 2268, 2304, 2448, 2736, 2880, 3312, 3600, 5040, 6300, 6480, 7056, 7920, 9072, 9360, 10800, 11088, 11520, 12240

Offset: 1

Author

Amiram Eldar, Oct 09 2021

Keywords

• nonn

Comments

The corresponding record values are 0, 2, 3, 8, 14, 16, 41, 56, 84, 87, 112, ...

Examples

			The first 9 values of A348271(k) for k = 1 to 9 are: 0, 0, 0, 2, 0, 0, 0, 0 and 3. The record values, 0, 2 and 3, occur at 1, 4 and 9, the first 3 terms of this sequence.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..500

Crossrefs

Cf. A348271.

The noninfinitary version of A002093.

Similar sequences: A285614, A292983, A327634, A328134, A329883.

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={}; sm = -1; Do[s1 = s[n];If[s1 > sm, sm= s1; AppendTo[seq, n]], {n, 1, 10^4}]; seq