A372724 Numbers k such that k = Sum_{j=2..k+2} L(k/prime(j)) where L(n/p) is the Legendre symbol. Fixed points of A372725.

0, 9, 25, 36, 49, 81, 100, 121, 144, 169, 196, 289, 324, 361, 400, 484, 529, 576, 625, 676, 729, 784, 841, 961, 1156, 1296, 1369, 1444, 1600, 1681, 1849, 1936, 2116, 2209, 2304, 2401, 2500, 2704, 2809, 2916, 3136, 3364, 3481, 3721, 3844, 4489, 4624, 5041, 5184, 5329, 5476, 5776

Offset: 1

Author

Peter Luschny, May 22 2024

Keywords

• nonn

Links

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

Crossrefs

Subsequence of A000290, and A069562 U {0}.

Cf. A372725, A336101, A373087.

Programs

Maple

L := (n, k) -> NumberTheory:-LegendreSymbol(n, ithprime(k)):
s := n -> local k; add(L(n, k), k = 2..n + 2):
select(m -> m = s(m), [seq(0..400)]);
# Alternative:
isA := k -> (k = 0) or (issqr(k) and
       nops(NumberTheory:-PrimeFactors(k/2^padic[ordp] (k, 2))) = 1):
select(isA, [seq(0..6000)]);

Mathematica

Join[{0}, Select[Range[100]^2, PrimeNu[#/2^IntegerExponent[#, 2]] == 1 &]] (* Paolo Xausa, Jul 10 2024 *)

PARI

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

Formula

A positive k is a term if k is a square and its odd part is divisible by exactly one prime.