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

Author

Amiram Eldar, Feb 06 2024

Keywords

• nonn
• easy

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

Crossrefs

Cf. A000290, A013661, A051903.

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

Similar sequences: A368714, A369938, A369939.

Cf. A361177, A366762, A369210.

Programs

Mathematica

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

PARI

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