A374589 Numbers whose maximum exponent in their prime factorization is a powerful number larger than 1.

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

Author

Amiram Eldar, Jul 12 2024

Keywords

• nonn
• easy

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

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

Crossrefs

Cf. A001694, A051903, A262276, A361177.

Subsequence of A013929, A130897 and A372405.

Similar sequences: A368714, A369937, A369938, A369939, A374588, A374590.

Programs

Mathematica

powQ[n_] := Min[FactorInteger[n][[;; , 2]]] > 1; q[n_] := powQ[Max[ FactorInteger[n][[;; , 2]] ]]; Select[Range[1200], q]

PARI

ispow(n) = n > 1 && ispowerful(n);
is(n) = n > 1 && ispow(vecmax(factor(n)[, 2]))