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

1,2

Comments

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

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

Example

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.

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

Crossrefs

Cf. A160135, A348604.

The nonexponential version of A002093.

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

Sequence in context: A046288 A076763 A064712 * A284667 A315132 A352101

Adjacent sequences: A348626 A348627 A348628 * A348630 A348631 A348632

Keyword

nonn

Author

Amiram Eldar, Oct 26 2021

Status

approved