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Numbers whose maximal exponent in their prime factorization is square.
8

%I #7 Feb 06 2024 08:14:31

%S 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,

%T 38,39,41,42,43,46,47,48,51,53,55,57,58,59,61,62,65,66,67,69,70,71,73,

%U 74,77,78,79,80,81,82,83,85,86,87,89,91,93,94,95,97,101,102

%N Numbers whose maximal exponent in their prime factorization is square.

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

%C Numbers k such that A051903(k) is square.

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

%H Amiram Eldar, <a href="/A369937/b369937.txt">Table of n, a(n) for n = 1..10000</a>

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

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

%Y Cf. A000290, A013661, A051903.

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

%Y Similar sequences: A368714, A369938, A369939.

%Y Cf. A361177, A366762, A369210.

%K nonn,easy

%O 1,2

%A _Amiram Eldar_, Feb 06 2024