A215284 Numbers m such that Sum_{k=1..m} (m - k | k) = 0, where (i|j) is the Kronecker symbol.

5, 8, 12, 18, 20, 21, 24, 28, 32, 40, 44, 48, 52, 53, 56, 60, 68, 69, 72, 76, 77, 80, 84, 88, 92, 96, 99, 104, 108, 112, 116, 120, 124, 125, 126, 128, 132, 136, 140, 141, 148, 150, 152, 156, 160, 162, 164, 165, 168, 172, 176, 180, 184, 188, 189, 192, 197

Offset: 1

Author

Peter Luschny, Aug 07 2012

Keywords

• nonn

Comments

Appears to include all multiples of 4 that are not squares. - Robert Israel, Mar 11 2018

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..2830 from Robert Israel)

Crossrefs

Cf. A215200, A215283, A215285.

Programs

Maple

f:= n -> add(numtheory:-jacobi(n-k,k),k=1..n):
select(n -> f(n)=0, [$1..300]); # Robert Israel, Mar 11 2018

Mathematica

Select[ Range[200], Sum[ KroneckerSymbol[# - k, k], {k, 1, #}] == 0 & ] (* Jean-François Alcover, Jul 29 2013 *)

PARI

is(m) = sum(k = 1, m, kronecker(m-k, k)) == 0; \\ Amiram Eldar, Nov 07 2024

Sage

def A215200_row(n): return [kronecker_symbol(n-k, k) for k in (1..n)]
[n for n in (1..197) if sum(A215200_row(n)) == 0]