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

1,2

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

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

Prog

(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

Crossrefs

Subsequence of A025487.

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

Sequence in context: A281016 A048169 A089882 * A206375 A146541 A363014

Adjacent sequences: A335847 A335848 A335849 * A335851 A335852 A335853

Keyword

nonn

Author

Amiram Eldar, Jun 26 2020

Status

approved