A124896 Number of squarefree numbers of the form n^2 + k^2, 1<=k<=n.

1, 1, 2, 1, 4, 2, 5, 4, 6, 4, 9, 3, 11, 6, 7, 7, 14, 5, 16, 8, 11, 8, 19, 7, 20, 11, 16, 12, 24, 8, 26, 15, 18, 15, 23, 11, 33, 16, 21, 15, 34, 10, 38, 19, 23, 20, 41, 15, 38, 19, 29, 22, 46, 15, 38, 22, 33, 26, 53, 15, 52, 26, 32, 30, 48, 18, 59, 30, 40, 22, 62, 21, 64, 32, 39, 34

Offset: 1

Author

Reinhard Zumkeller, Nov 12 2006

Keywords

• nonn
• look

Comments

a(n) = Sum(A008966(A070216(n,k)):1<=k<=n) = Sum(ABS(A124895(n,k)):1<=k<=n).

0 < a(n) <= n-1.

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A008966, A070216, A124895.

Programs

Maple

f:= proc(n) local k; nops(select(numtheory:-issqrfree, [seq(n^2+k^2,k=1..n)])) end proc:
map(f, [$1..100]); # Robert Israel, Dec 18 2024

Mathematica

Count[#,?SquareFreeQ]&/@Table[n^2+k^2,{n,80},{k,n}] (* _Harvey P. Dale, Mar 30 2012 *)

PARI

a(n) = sum(k=1, n, issquarefree(n^2 + k^2)); \\ Michel Marcus, Dec 18 2024