cp's OEIS Frontend

A381950 Odd numbers whose prime factorization has an even maximum exponent.

%I A381950 #10 Mar 12 2025 08:24:10
%S A381950 1,9,25,45,49,63,75,81,99,117,121,147,153,169,171,175,207,225,245,261,
%T A381950 275,279,289,315,325,333,361,363,369,387,405,423,425,441,475,477,495,
%U A381950 507,525,529,531,539,549,567,575,585,603,605,625,637,639,657,693,711,725
%N A381950 Odd numbers whose prime factorization has an even maximum exponent.
%C A381950 Odd numbers k such that A051903(k) is even.
%C A381950 The asymptotic density of this sequence is (1/2) * Sum_{k>=2} (-1)^k * (1 - 2^k/((2^k-1)*zeta(k))) = 0.075617194130991839249... .
%H A381950 Amiram Eldar, <a href="/A381950/b381950.txt">Table of n, a(n) for n = 1..10000</a>
%e A381950 9 = 3^2 is a term since it is odd and 2 is even.
%e A381950 45 = 3^2 * 5 is a term since it is odd and 2 is even.
%e A381950 125 = 5^3 is not a term since 3 is odd.
%t A381950 Select[Range[1, 1000, 2], # == 1 || EvenQ[Max[FactorInteger[#][[;; , 2]]]] &]
%o A381950 (PARI) isok(k) = if(k == 1, 1, k % 2 && !(vecmax(factor(k)[, 2]) % 2));
%Y A381950 Intersection of A005408 and A368714.
%Y A381950 Subsequence of A381956.
%Y A381950 A381823 is a subsequence.
%Y A381950 Cf. A051903, A375039, A381951.
%K A381950 nonn,easy
%O A381950 1,2
%A A381950 _Amiram Eldar_, Mar 11 2025