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URL: https://oeis.org/A378988

⇱ A378988 - OEIS

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A378988
a(n) = 2*n XOR 1+sigma(n), where XOR is bitwise-xor, A003987.
4
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.
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)].
Sequence in context: A268904 A058896 A186748 * A222754 A181905 A350826
KEYWORD
nonn,look
AUTHOR
Antti Karttunen, Dec 16 2024
STATUS
approved