A335850 Cubefull highly composite numbers: numbers with a record number of cubefull divisors (A190867).

1, 8, 16, 32, 64, 128, 256, 512, 1024, 1728, 2592, 5184, 7776, 10368, 15552, 20736, 31104, 46656, 62208, 93312, 124416, 186624, 248832, 373248, 559872, 746496, 1119744, 1492992, 2239488, 2985984, 3359232, 4478976, 6718464, 8957952, 13436928, 17915904, 26873856

Offset: 1

Author

Amiram Eldar, Jun 26 2020

Keywords

• nonn

Comments

The analogous sequence of squarefull highly composite numbers is the sequence of highly powerful numbers (A005934).

The corresponding record values are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 15, 16, ... (see the link for more values).

Also, indices of records in A361430, i.e., numbers k with a record number of coreful divisors d such that k/d is also a coreful divisor of k (a coreful divisor d of a number k is a divisor with the same set of distinct prime factors as k, see A307958). - Amiram Eldar, Aug 15 2023

Links

• Amiram Eldar, Table of n, a(n) for n = 1..832
• Amiram Eldar, Table of n, a(n), A190867(a(n)) for n = 1..832

Crossrefs

Subsequence of A025487.

Cf. A002182, A005934, A190867, A307958, A361430.

Programs

Mathematica

f[p_, e_] := Max[1, e-1] ; d[1] = 1; d[n_] := Times @@ (f @@@ FactorInteger[n]); s = {}; dm = 0; Do[d1 = d[n]; If[d1 > dm, dm = d1; AppendTo[s, n]], {n, 1, 10^5}]; s

PARI

d(n) = vecprod(apply(x->max(1, x-1), factor(n)[, 2]));
lista(kmax) = {my(dm = 0, d1); for(k = 1, kmax, d1 = d(k); if(d1 > dm, dm = d1; print1(k, ", ")));} \\ Amiram Eldar, Aug 15 2023