A372724 -id:A372724 - cp's OEIS frontend

A372725 a(n) = Sum_{k=2..n+2} L(n/prime(k)) where L(n/p) is the Legendre symbol. Row sums of A372726.

0, 2, -1, -1, 5, -3, -2, -3, -3, 9, -2, -3, -4, -3, -2, -2, 17, -3, -4, -1, -2, 0, -4, -1, 0, 25, -4, -1, -4, -5, -3, -5, -3, -6, -2, 2, 36, -1, 6, -4, -6, -7, 1, -3, -4, -2, 0, 9, -4, 49, -4, -4, -4, -7, -6, -4, -2, -6, -4, -3, 1, 1, 12, -4, 65, -2, -5, -5

Offset: 0

Peter Luschny, May 22 2024

sign

Paolo Xausa, Table of n, a(n) for n = 0..10000

Cf. A372726, A372724 (fixed points).

L := (n, k) -> NumberTheory:-LegendreSymbol(n, ithprime(k)):
seq(add(L(n, k), k = 2..n + 2), n = 0..67);

A372725[n_] := Sum[JacobiSymbol[n, Prime[k]], {k, 2, n + 2}];
Array[A372725, 100, 0] (* Paolo Xausa, Jul 10 2024 *)

a(n) = sum(k=2, n+2, kronecker(n, prime(k))); \\ Michel Marcus, May 22 2024

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

Original entry on oeis.org

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

Peter Luschny, May 23 2024

nonn

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

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

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

Cf. A000290, A098904, A372724, A336101.

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

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

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

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

cp's OEIS Frontend

A372725 a(n) = Sum_{k=2..n+2} L(n/prime(k)) where L(n/p) is the Legendre symbol. Row sums of A372726.

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