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A374588
Numbers whose maximum exponent in their prime factorization is a composite number.
3
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
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
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);
is(n) = n > 1 && iscomposite(vecmax(factor(n)[, 2]));
CROSSREFS
Complement of A074661 within A013929.
Subsequence of A322448 and A322449 \ {1}.
Similar sequences: A368714, A369937, A369938, A369939, A374589, A374590.
Sequence in context: A373286 A260985 A322448 * A354181 A264164 A045047
KEYWORD
nonn,easy
AUTHOR
Amiram Eldar, Jul 12 2024
STATUS
approved