login
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.
3
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
1,2
FORMULA
A positive k is a term if k is a square and its odd part is divisible by exactly one prime.
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 *)
PROG
(PARI) isok(k) = k == sum(j=2, k+2, kronecker(k, prime(j))); \\ Michel Marcus, May 22 2024
CROSSREFS
Subsequence of A000290, and A069562 U {0}.
Sequence in context: A137190 A044070 A376217 * A348234 A226647 A147199
KEYWORD
nonn
AUTHOR
Peter Luschny, May 22 2024
STATUS
approved