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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.

%I A372724 #23 Oct 07 2024 02:04:16
%S A372724 0,9,25,36,49,81,100,121,144,169,196,289,324,361,400,484,529,576,625,
%T A372724 676,729,784,841,961,1156,1296,1369,1444,1600,1681,1849,1936,2116,
%U A372724 2209,2304,2401,2500,2704,2809,2916,3136,3364,3481,3721,3844,4489,4624,5041,5184,5329,5476,5776
%N 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.
%H A372724 Paolo Xausa, <a href="/A372724/b372724.txt">Table of n, a(n) for n = 1..10000</a>
%F A372724 A positive k is a term if k is a square and its odd part is divisible by exactly one prime.
%p A372724 L := (n, k) -> NumberTheory:-LegendreSymbol(n, ithprime(k)):
%p A372724 s := n -> local k; add(L(n, k), k = 2..n + 2):
%p A372724 select(m -> m = s(m), [seq(0..400)]);
%p A372724 # Alternative:
%p A372724 isA := k -> (k = 0) or (issqr(k) and
%p A372724        nops(NumberTheory:-PrimeFactors(k/2^padic[ordp] (k, 2))) = 1):
%p A372724 select(isA, [seq(0..6000)]);
%t A372724 Join[{0}, Select[Range[100]^2, PrimeNu[#/2^IntegerExponent[#, 2]] == 1 &]] (* _Paolo Xausa_, Jul 10 2024 *)
%o A372724 (PARI) isok(k) = k == sum(j=2, k+2, kronecker(k, prime(j))); \\ _Michel Marcus_, May 22 2024
%Y A372724 Subsequence of A000290, and A069562 U {0}.
%Y A372724 Cf. A372725, A336101, A373087.
%K A372724 nonn
%O A372724 1,2
%A A372724 _Peter Luschny_, May 22 2024