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A373087 k is a term if k is a square and its odd part is divisible by exactly two distinct primes.

%I A373087 #31 Oct 30 2024 07:10:59
%S A373087 225,441,900,1089,1225,1521,1764,2025,2601,3025,3249,3600,3969,4225,
%T A373087 4356,4761,4900,5625,5929,6084,7056,7225,7569,8100,8281,8649,9025,
%U A373087 9801,10404,12100,12321,12996,13225,13689,14161,14400,15129,15876,16641,16900,17424,17689,18225
%N A373087 k is a term if k is a square and its odd part is divisible by exactly two distinct primes.
%C A373087 The sequence b with terms b(n)=2*sqrt(a(n)) is a subsequence of A098904. - _Hugo Pfoertner_, Jun 01 2024
%H A373087 Paolo Xausa, <a href="/A373087/b373087.txt">Table of n, a(n) for n = 1..10000</a>
%F A373087 a(n) = Sum_{k=2..n+3} LegendreSymbol(n, prime(k)).
%e A373087 8100 is a term because (8100 / 2^2) = 3^4 * 5^2.
%p A373087 isA := k -> issqr(k) and nops(NumberTheory:-PrimeFactors(k/2^padic[ordp](k, 2))) = 2: A := select(isA, [seq(1..19000)]);
%t A373087 Select[Range[200]^2, PrimeNu[#/2^IntegerExponent[#, 2]] == 2 &] (* _Paolo Xausa_, Jul 10 2024 *)
%o A373087 (PARI) isok(k) = issquare(k) && (omega(k/2^valuation(k,2)) == 2); \\ _Michel Marcus_, May 31 2024
%Y A373087 Cf. A000290, A098904, A372724, A336101.
%K A373087 nonn
%O A373087 1,1
%A A373087 _Peter Luschny_, May 23 2024