A335850 - OEIS

%I #14 Aug 15 2023 07:43:33

%S 1,8,16,32,64,128,256,512,1024,1728,2592,5184,7776,10368,15552,20736,

%T 31104,46656,62208,93312,124416,186624,248832,373248,559872,746496,

%U 1119744,1492992,2239488,2985984,3359232,4478976,6718464,8957952,13436928,17915904,26873856

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

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

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

%C 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

%H Amiram Eldar, <a href="/A335850/b335850.txt">Table of n, a(n) for n = 1..832</a>

%H Amiram Eldar, <a href="/A335850/a335850.txt">Table of n, a(n), A190867(a(n)) for n = 1..832</a>

%t 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

%o (PARI) d(n) = vecprod(apply(x->max(1, x-1), factor(n)[, 2]));

%o 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

%Y Subsequence of A025487.

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

%K nonn

%O 1,2

%A _Amiram Eldar_, Jun 26 2020