A348629 Nonexponential highly abundant numbers: numbers m such that nesigma(m) > nesigma(k) for all k < m, where nesigma(k) is the sum of nonexponential divisors of n (A160135).

1, 6, 10, 12, 18, 24, 30, 42, 48, 54, 60, 78, 84, 90, 96, 120, 168, 192, 210, 240, 270, 312, 330, 360, 384, 420, 480, 630, 672, 840, 960, 1056, 1080, 1248, 1320, 1440, 1560, 1680, 1890, 1920, 2280, 2310, 2400, 2520, 2640, 2688, 3000, 3120, 3240, 3360, 4200, 4320

Offset: 1

Author

Amiram Eldar, Oct 26 2021

Keywords

• nonn

Comments

The corresponding record values are 1, 6, 8, 10, 15, 30, 42, 54, 58, 60, 78, ... (see the link for more values).

Examples

			The first 6 values of nesigma(k), for k = 1 to 6 are 1, 1, 1, 1, 1 and 6. The record values, 1 and 6, occur at 1 and 6, the first 2 terms of this sequence.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..577
• Amiram Eldar, Table of n, a(n), A160135(a(n)) for n = 1..577

Crossrefs

Cf. A160135, A348604.

The nonexponential version of A002093.

Similar sequences: A285614, A292983, A327634, A328134, A329883, A348272.

Programs

Mathematica

esigma[n_] := Times @@ (Sum[First[#]^d, {d, Divisors[Last[#]]}] &) /@ FactorInteger[n]; s[1] = 1; s[n_] := DivisorSigma[1, n] - esigma[n]; seq = {}; sm = -1; Do[s1 = s[n]; If[s1 > sm, sm = s1; AppendTo[seq, n]], {n, 1, 10^4}]; seq