A378988 a(n) = 2*n XOR 1+sigma(n), where XOR is bitwise-xor, A003987.

0, 0, 3, 0, 13, 1, 7, 0, 28, 7, 27, 5, 21, 5, 7, 0, 49, 12, 51, 3, 11, 9, 55, 13, 18, 31, 31, 1, 37, 117, 31, 0, 115, 115, 119, 20, 109, 113, 119, 11, 121, 53, 123, 13, 21, 21, 111, 29, 88, 58, 47, 11, 93, 21, 39, 9, 35, 47, 75, 209, 69, 29, 23, 0, 215, 21, 195, 247, 235, 29, 199, 84, 217, 231, 235, 21, 251, 53, 207

Offset

1,3

Comments

For any hypothetical quasiperfect number q (for which sigma(q) = 2*q+1, see A336701), a(q) would be equal to 2*q XOR 2*q+2 = 2*(q XOR q+1) = 2*A038712(1+q) = A100892(1+q).

See also A000079 and A235796 concerning the "almost perfect" or "least deficient" numbers that give positions of 0's here.

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).

Formula

For all n in A028983, a(n) = 2n+1 XOR sigma(n) = 1+A318467(n).

Mathematica

Array[BitXor[2*#, DivisorSigma[1, #] + 1] &, 100] (* Paolo Xausa, Dec 16 2024 *)

Prog

(PARI) A378988(n) = bitxor(n+n, 1+sigma(n));

Crossrefs

Cf. A000079 (conjectured to give positions of all 0's), A000396 (positions of 1's), A000203, A003987, A028982 (positions of even terms), A028983 (of odd terms), A038712, A100892, A318467, A336701, A378998, A379009 [= a(n^2)].

Cf. also A235796, A294898, A294899, A318457.

Sequence in context: A268904 A058896 A186748 * A222754 A181905 A350826

Adjacent sequences: A378985 A378986 A378987 * A378989 A378990 A378991

Keyword

nonn,look

Author

Antti Karttunen, Dec 16 2024

Status

approved