A369937 Numbers whose maximal exponent in their prime factorization is square.

1, 2, 3, 5, 6, 7, 10, 11, 13, 14, 15, 16, 17, 19, 21, 22, 23, 26, 29, 30, 31, 33, 34, 35, 37, 38, 39, 41, 42, 43, 46, 47, 48, 51, 53, 55, 57, 58, 59, 61, 62, 65, 66, 67, 69, 70, 71, 73, 74, 77, 78, 79, 80, 81, 82, 83, 85, 86, 87, 89, 91, 93, 94, 95, 97, 101, 102

Offset

1,2

Comments

First differs from A366762 at n = 84, and from A197680, A361177 and A369210 at n = 95.

Numbers k such that A051903(k) is square.

The asymptotic density of this sequence is 1/zeta(2) + Sum_{k>=2} (1/zeta(k^2+1) - 1/zeta(k^2)) = 0.64939447949574562687... .

Links

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

Mathematica

Select[Range[100], IntegerQ@ Sqrt[Max[FactorInteger[#][[;; , 2]]]] &]

Prog

(PARI) lista(kmax) = for(k = 1, kmax, if(k == 1 || issquare(vecmax(factor(k)[, 2])), print1(k, ", ")));

Crossrefs

Cf. A000290, A013661, A051903.

Subsequences: A002416, A005117, A030514, A030635, A113849, A178739, A179665, A179692, A197680.

Similar sequences: A368714, A369938, A369939.

Cf. A361177, A366762, A369210.

Sequence in context: A361177 A366762 A369210 * A119024 A321453 A374038

Adjacent sequences: A369934 A369935 A369936 * A369938 A369939 A369940

Keyword

nonn,easy

Author

Amiram Eldar, Feb 06 2024

Status

approved