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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). 2

%I #14 Oct 26 2021 16:52:39

%S 1,6,10,12,18,24,30,42,48,54,60,78,84,90,96,120,168,192,210,240,270,

%T 312,330,360,384,420,480,630,672,840,960,1056,1080,1248,1320,1440,

%U 1560,1680,1890,1920,2280,2310,2400,2520,2640,2688,3000,3120,3240,3360,4200,4320

%N 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).

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

%H Amiram Eldar, <a href="/A348629/b348629.txt">Table of n, a(n) for n = 1..577</a>

%H Amiram Eldar, <a href="/A348629/a348629.txt">Table of n, a(n), A160135(a(n)) for n = 1..577</a>

%e 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.

%t 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

%Y Cf. A160135, A348604.

%Y The nonexponential version of A002093.

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

%K nonn

%O 1,2

%A _Amiram Eldar_, Oct 26 2021

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Last modified March 28 08:22 EDT 2024. Contains 371236 sequences. (Running on oeis4.)