A363330 - OEIS

%I #9 May 28 2023 20:50:13

%S 1,8,128,216,3456,27000,279936,432000,9261000,34992000,148176000,

%T 8957952000,12002256000,197222256000,3072577536000,7501410000000,

%U 15975002736000,433297296432000,1920360960000000,4089600700416000,9984376710000000,35097081010992000,2128789617370416000

%N Numbers with a record number of divisors that are both coreful and infinitary.

%C Indices of records in A363329.

%C The corresponding record values are 1, 3, 7, 9, 21, 27, 49, 63, 81, 147, 189, 315, ... (see the link for more values).

%H Amiram Eldar, <a href="/A363330/b363330.txt">Table of n, a(n) for n = 1..64</a>

%H Amiram Eldar, <a href="/A363330/a363330.txt">Table of n, a(n), A363329(a(n)) for n = 1..64</a>

%t f[p_, e_] := 2^DigitCount[e, 2, 1] - 1; d[1] = 1; d[n_] := Times @@ f @@@ FactorInteger[n];

%t v = Cases[Import["https://oeis.org/A025487/b025487.txt", "Table"], {_, _}][[;; , 2]];

%t seq = {}; dm = 0; Do[If[(dk = d[v[[k]]]) > dm, dm = dk; AppendTo[seq, v[[k]]]], {k, 1, Length[v]}]; seq

%Y Cf. A363329.

%Y Subsequence of A025487.

%Y Similar sequences: A005934, A037992.

%K nonn

%O 1,2

%A _Amiram Eldar_, May 28 2023