A392279 Numbers whose maximum exponent in their prime factorization is a nonsquarefree number.

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

First differs from its subsequence A374589 at n = 178: a(178) = 4096 = 2^12 is not a term in A374589.

Subsequence of A130897 and first differs from it at n = 115: A130897(115) = 2592 = 2^5 * 3^4 is not a term in this sequence.

Numbers k such that A051903(k) is a term in A013929.

The asymptotic density of this sequence is Sum_{k >= 1 and in A013929} (1/zeta(k+1) - 1/zeta(k)) = Sum_{k>=2} (1-mu(k)^2)*(1/zeta(k+1) - 1/zeta(k)) = 1 + Sum_{k>=2} (mu(k)^2-mu(k-1)^2)/zeta(k) = 0.043649558573353714635... .

Links

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

Mathematica

q[k_] := !SquareFreeQ[Max[FactorInteger[k][[;; , 2]]]]; Select[Range[1200], q]

Prog

(PARI) isok(k) = k > 1 && !issquarefree(vecmax(factor(k)[, 2]));

Crossrefs

Subsequence of A130897.

A374589 is a subsequence.

Cf. A008683 (mu), A013929, A051903.

Sequence in context: A348882 A130897 A374589 * A336595 A386804 A383264

Adjacent sequences: A392276 A392277 A392278 * A392280 A392281 A392282

Keyword

nonn,easy

Author

Amiram Eldar, Jan 06 2026

Status

approved