A379009 a(n) = 2*n^2 XOR 1+sigma(n^2).

0, 0, 28, 0, 18, 20, 88, 0, 216, 18, 116, 180, 490, 24, 86, 0, 886, 472, 940, 226, 404, 108, 1544, 756, 2028, 74, 500, 200, 1530, 3086, 1120, 0, 3648, 366, 3962, 1160, 3890, 292, 686, 994, 2974, 6540, 2324, 7996, 378, 8104, 6544, 3060, 6192, 1748, 7114, 778, 7874, 2860, 1982, 1224, 2616, 3482, 5860, 11502, 5082

Offset: 1

Author

Antti Karttunen, Dec 16 2024

Keywords

• nonn

Comments

For any hypothetical quasiperfect number q^2 (for which sigma(q^2) = 2*q^2 + 1, which are known to be odd squares if they exist at all, see references in A336701), a(q) would be equal to 2*q^2 XOR 2*(q^2)+2 = 2*(q^2 XOR q^2+1) = 2*A038712(1+q^2) = 2*3 = 6.

a(n) = 0 if n^2 is a square that is "almost perfect", also known as "least deficient". Only known examples are powers of 2. See A000079, A033879.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..32768
• Index entries for sequences related to binary expansion of n.
• Index entries for sequences related to sigma(n).

Crossrefs

Cf. A000079 (conjectured to give positions of all 0's), A000290, A003987, A033879, A065764, A336701, A378988.

Cf. also A378999, A379007.

Programs

Mathematica

Map[BitXor[2*#, DivisorSigma[1, #] + 1] &, Range[100]^2] (* Paolo Xausa, Dec 18 2024 *)

PARI

A379009(n) = bitxor(2*(n^2),1+sigma(n^2));

Formula

a(n) = A378988(A000290(n)).