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

225, 441, 900, 1089, 1225, 1521, 1764, 2025, 2601, 3025, 3249, 3600, 3969, 4225, 4356, 4761, 4900, 5625, 5929, 6084, 7056, 7225, 7569, 8100, 8281, 8649, 9025, 9801, 10404, 12100, 12321, 12996, 13225, 13689, 14161, 14400, 15129, 15876, 16641, 16900, 17424, 17689, 18225

Offset: 1

Author

Peter Luschny, May 23 2024

Keywords

• nonn

Comments

The sequence b with terms b(n)=2*sqrt(a(n)) is a subsequence of A098904. - Hugo Pfoertner, Jun 01 2024

Examples

			8100 is a term because (8100 / 2^2) = 3^4 * 5^2.
		

Links

• Paolo Xausa, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000290, A098904, A372724, A336101.

Programs

Maple

isA := k -> issqr(k) and nops(NumberTheory:-PrimeFactors(k/2^padic[ordp](k, 2))) = 2: A := select(isA, [seq(1..19000)]);

Mathematica

Select[Range[200]^2, PrimeNu[#/2^IntegerExponent[#, 2]] == 2 &] (* Paolo Xausa, Jul 10 2024 *)

PARI

isok(k) = issquare(k) && (omega(k/2^valuation(k,2)) == 2); \\ Michel Marcus, May 31 2024

Formula

a(n) = Sum_{k=2..n+3} LegendreSymbol(n, prime(k)).