A215284 - OEIS

%I #22 Nov 07 2024 08:32:35

%S 5,8,12,18,20,21,24,28,32,40,44,48,52,53,56,60,68,69,72,76,77,80,84,

%T 88,92,96,99,104,108,112,116,120,124,125,126,128,132,136,140,141,148,

%U 150,152,156,160,162,164,165,168,172,176,180,184,188,189,192,197

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

%C Appears to include all multiples of 4 that are not squares. - _Robert Israel_, Mar 11 2018

%H Amiram Eldar, <a href="/A215284/b215284.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..2830 from Robert Israel)

%p f:= n -> add(numtheory:-jacobi(n-k,k),k=1..n):

%p select(n -> f(n)=0, [$1..300]); # _Robert Israel_, Mar 11 2018

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

%o (Sage)

%o def A215200_row(n): return [kronecker_symbol(n-k, k) for k in (1..n)]

%o [n for n in (1..197) if sum(A215200_row(n)) == 0]

%o (PARI) is(m) = sum(k = 1, m, kronecker(m-k, k)) == 0; \\ _Amiram Eldar_, Nov 07 2024

%Y Cf. A215200, A215283, A215285.

%K nonn

%O 1,1

%A _Peter Luschny_, Aug 07 2012