A374588 - OEIS

A374588

Numbers whose maximum exponent in their prime factorization is a composite number.

16, 48, 64, 80, 81, 112, 144, 162, 176, 192, 208, 240, 256, 272, 304, 320, 324, 336, 368, 400, 405, 432, 448, 464, 496, 512, 528, 560, 567, 576, 592, 624, 625, 648, 656, 688, 704, 720, 729, 752, 768, 784, 810, 816, 832, 848, 880, 891, 912, 944, 960, 976, 1008

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OFFSET

1,1

COMMENTS

Subsequence of A322448 and first differs from it at n = 138: A322448(138) = 2592 = 2^5 * 3^4 is not a term of this sequence.

The asymptotic density of this sequence is d = Sum_{k composite} (1/zeta(k+1) - 1/zeta(k)) = 0.05296279266796920306... . The asymptotic density of this sequence within the nonsquarefree numbers (A013929) is d / (1 - 1/zeta(2)) = 0.13508404411123191108... .

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..10000

MAPLE

filter:= proc(n) local m;

m:= max(ifactors(n)[2][.., 2]);

m > 1 and not isprime(m)

end proc:

select(filter, [$1..10000]); # Robert Israel, Jul 14 2024

MATHEMATICA

Select[Range[1200], CompositeQ[Max[FactorInteger[#][[;; , 2]]]] &]

PROG

(PARI) iscomposite(n) = n > 1 && !isprime(n);