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A335850
Cubefull highly composite numbers: numbers with a record number of cubefull divisors (A190867).
2
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
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.
Sequence in context: A281016 A048169 A089882 * A206375 A146541 A363014
KEYWORD
nonn
AUTHOR
Amiram Eldar, Jun 26 2020
STATUS
approved