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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
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified May 24 14:36 EDT 2022. Contains 354037 sequences. (Running on oeis4.)