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
Keywords
Links
- Paolo Xausa, Table of n, a(n) for n = 1..10000
Programs
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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.