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

1,1

Comments

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

Links

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

Formula

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

Example

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

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 *)

Prog

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

Crossrefs

Cf. A000290, A098904, A372724, A336101.

Sequence in context: A207640 A267892 A363217 * A216419 A390955 A246199

Adjacent sequences: A373084 A373085 A373086 * A373088 A373089 A373090

Keyword

nonn

Author

Peter Luschny, May 23 2024

Status

approved