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A369937
Numbers whose maximal exponent in their prime factorization is square.
8
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
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
KEYWORD
nonn,easy
AUTHOR
Amiram Eldar, Feb 06 2024
STATUS
approved