cp's OEIS Frontend

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).

%I A348629 #14 Oct 26 2021 16:52:39
%S A348629 1,6,10,12,18,24,30,42,48,54,60,78,84,90,96,120,168,192,210,240,270,
%T A348629 312,330,360,384,420,480,630,672,840,960,1056,1080,1248,1320,1440,
%U A348629 1560,1680,1890,1920,2280,2310,2400,2520,2640,2688,3000,3120,3240,3360,4200,4320
%N 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).
%C A348629 The corresponding record values are 1, 6, 8, 10, 15, 30, 42, 54, 58, 60, 78, ... (see the link for more values).
%H A348629 Amiram Eldar, <a href="/A348629/b348629.txt">Table of n, a(n) for n = 1..577</a>
%H A348629 Amiram Eldar, <a href="/A348629/a348629.txt">Table of n, a(n), A160135(a(n)) for n = 1..577</a>
%e A348629 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 A348629 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 A348629 Cf. A160135, A348604.
%Y A348629 The nonexponential version of A002093.
%Y A348629 Similar sequences: A285614, A292983, A327634, A328134, A329883, A348272.
%K A348629 nonn
%O A348629 1,2
%A A348629 _Amiram Eldar_, Oct 26 2021