A348272 - OEIS

%I #8 Oct 13 2021 10:31:37

%S 1,4,9,12,16,28,36,48,80,100,112,144,180,240,300,324,336,396,400,432,

%T 468,528,576,684,720,900,1008,1200,1296,1584,1872,2160,2268,2304,2448,

%U 2736,2880,3312,3600,5040,6300,6480,7056,7920,9072,9360,10800,11088,11520,12240

%N Noninfinitary highly abundant numbers: numbers m such that nisigma(m) > nisigma(k) for all k < m, where nisigma(k) is the sum of noninfinitary divisors of n (A348271).

%C The corresponding record values are 0, 2, 3, 8, 14, 16, 41, 56, 84, 87, 112, ...

%H Amiram Eldar, <a href="/A348272/b348272.txt">Table of n, a(n) for n = 1..500</a>

%e The first 9 values of A348271(k) for k = 1 to 9 are: 0, 0, 0, 2, 0, 0, 0, 0 and 3. The record values, 0, 2 and 3, occur at 1, 4 and 9, the first 3 terms of this sequence.

%t f[p_, e_] := Module[{b = IntegerDigits[e, 2], m}, m = Length[b]; Product[If[b[[j]] > 0, 1 + p^(2^(m - j)), 1], {j, 1, m}]]; isigma[1] = 1; isigma[n_] := Times @@ f @@@ FactorInteger[n]; s[n_] := DivisorSigma[1,n] - isigma[n]; seq={}; sm = -1; Do[s1 = s[n];If[s1 > sm, sm= s1; AppendTo[seq, n]], {n, 1, 10^4}]; seq

%Y Cf. A348271.

%Y The noninfinitary version of A002093.

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

%K nonn

%O 1,2

%A _Amiram Eldar_, Oct 09 2021