A377879 Deficiency of squares: a(n) = 2n^2 - sigma(n^2).

1, 1, 5, 1, 19, -19, 41, 1, 41, -17, 109, -115, 155, -7, 47, 1, 271, -199, 341, -161, 141, 37, 505, -499, 469, 71, 365, -199, 811, -1021, 929, 1, 449, 163, 683, -1159, 1331, 221, 663, -737, 1639, -1659, 1805, -251, 299, 361, 2161, -2035, 2001, -467, 1211, -265, 2755, -1819, 1927, -967, 1545, 631, 3421, -5293, 3659, 737

Offset: 1

Author

Antti Karttunen, Nov 23 2024

Keywords

• sign

Comments

It is conjectured that 1's occur only when n is two's power (A000079), and that there are no -1's in this sequence. See comments in A033879 and in A337339.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20000
• Index entries for sequences related to sigma(n).

Crossrefs

Cf. A000290, A000079 (conjectured to give positions of all 1's), A033879, A378231 [= a(A003961(n))].

Cf. A000012, A083884.

Cf. also square array A083064.

Programs

Mathematica

Table[2n^2-DivisorSigma[1, n^2], {n, 62}] (* James C. McMahon, Nov 24 2024 *)

PARI

A033879(n) = (n+n-sigma(n));
A377879(n) = A033879(n*n);

Formula

a(n) = A033879(A000290(n)).