login
A374589
Numbers whose maximum exponent in their prime factorization is a powerful number larger than 1.
3
16, 48, 80, 81, 112, 144, 162, 176, 208, 240, 256, 272, 304, 324, 336, 368, 400, 405, 432, 464, 496, 512, 528, 560, 567, 592, 624, 625, 648, 656, 688, 720, 752, 768, 784, 810, 816, 848, 880, 891, 912, 944, 976, 1008, 1040, 1053, 1072, 1104, 1134, 1136, 1168, 1200
OFFSET
1,1
COMMENTS
Subsequence of A130897 and first differs from it at n = 115: A130897(115) = 2592 = 2^5 * 3^4 is not a term of this sequence.
The asymptotic density of this sequence is d = Sum_{k > 1 and in A001694} (1/zeta(k+1) - 1/zeta(k)) = 0.043523813088759413253... . The asymptotic density of this sequence within A130897 is d/(1 - A262276) = 0.98744988886705430331... .
LINKS
MATHEMATICA
powQ[n_] := Min[FactorInteger[n][[;; , 2]]] > 1; q[n_] := powQ[Max[ FactorInteger[n][[;; , 2]] ]]; Select[Range[1200], q]
PROG
(PARI) ispow(n) = n > 1 && ispowerful(n);
is(n) = n > 1 && ispow(vecmax(factor(n)[, 2]))
CROSSREFS
Subsequence of A013929, A130897 and A372405.
Similar sequences: A368714, A369937, A369938, A369939, A374588, A374590.
Sequence in context: A195087 A348882 A130897 * A336595 A069084 A084112
KEYWORD
nonn,easy
AUTHOR
Amiram Eldar, Jul 12 2024
STATUS
approved