A377709 - OEIS

%I #9 Nov 04 2024 20:50:03

%S 1,4,8,36,72,128,216,1152,3456,27000,28800,86400,279936,432000,

%T 4233600,6998400,21168000,34992000,148176000,342921600,1714608000,

%U 8957952000,12002256000,197222256000,207467568000,438939648000,1071630000000,1452272976000,3072577536000,7501410000000

%N Numbers that have a record number of infinitary divisors that are powerful (A001694).

%C Indices of records in A360721.

%C The corresponding record values are 1, 2, 3, 4, 6, 7, 9, 14, 21, 27, 28, 42, 49, 63, 84, 98, ... (see the link for more values).

%H Amiram Eldar, <a href="/A377709/b377709.txt">Table of n, a(n) for n = 1..117</a>

%H Amiram Eldar, <a href="/A377709/a377709.txt">Table of n, a(n), A360721(a(n)) for n = 1..117</a>

%t f[p_, e_] := 2^DigitCount[e, 2, 1] - Mod[e, 2]; d[1] = 1; d[n_] := Times @@ f @@@ FactorInteger[n]; v = Cases[Import["https://oeis.org/A025487/b025487.txt", "Table"], {_, _}][[;; , 2]]; seq = {}; dm = 0; Do[If[(dk = d[v[[k]]]) > dm, dm = dk; AppendTo[seq, v[[k]]]], {k, 1, Length[v]}]; seq

%Y Cf. A001694, A037445, A360721.

%Y Subsequence of A025487.

%K nonn

%O 1,2

%A _Amiram Eldar_, Nov 04 2024