A124895 -id:A124895 - cp's OEIS frontend

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

Reinhard Zumkeller, Nov 12 2006

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

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

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

Cf. A008966, A070216, A124895.

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

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

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

A124897 a(n) = mu(n^2 + 1), mu = A008683.

Original entry on oeis.org

-1, -1, 1, -1, 1, -1, 0, 1, 1, -1, 1, 1, -1, -1, 1, -1, -1, 0, 1, -1, -1, 1, -1, -1, 1, -1, -1, 1, 1, 1, -1, 0, -1, 1, 1, -1, -1, 0, 1, -1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 0, 1, 1, 1, 1, 1, -1, 1, 1, -1, -1, 0, 1, 0, 1, -1, 1, -1, -1, 1, -1, 1, 1, 1, -1, 0, 1, -1, 1, 1, -1, 1, -1, -1, -1, 1, 0, -1, 1, 1, -1, -1, 0, 1, 1, 1, -1, 1, -1, 1

Offset: 1

Reinhard Zumkeller, Nov 12 2006

sign

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A002522, A008683, A059592, A124895.

MoebiusMu[Range[107]^2+1] (* T. D. Noe, Nov 27 2006 *)

a(n) = moebius(n^2+1); \\ Michel Marcus, Jul 26 2022

a(n) = A008683(A002522(n)) = A124895(n,1);

a(n) = 0 iff A059592(n) > 1;

Corrected by T. D. Noe, Nov 27 2006

cp's OEIS Frontend

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

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