A318458 a(n) = n AND A001065(n), where AND is bitwise-and (A004198) & A001065 = sum of proper divisors.

0, 0, 1, 0, 1, 6, 1, 0, 0, 8, 1, 0, 1, 10, 9, 0, 1, 16, 1, 20, 1, 6, 1, 0, 0, 16, 9, 28, 1, 10, 1, 0, 1, 0, 1, 36, 1, 6, 1, 32, 1, 34, 1, 40, 33, 10, 1, 0, 0, 34, 17, 36, 1, 2, 17, 0, 17, 32, 1, 44, 1, 34, 41, 0, 1, 66, 1, 0, 1, 66, 1, 72, 1, 8, 1, 64, 1, 74, 1, 64, 0, 0, 1, 4, 21, 6, 1, 88, 1, 16, 17, 76, 1, 18, 25, 0, 1, 64, 33, 100, 1, 98, 1, 104, 65

Offset

1,6

Comments

The peculiar look of the scatterplot is partly an artifact of the logarithmic scale. Compare also to the scatterplot of A318468.

Links

Antti Karttunen, Table of n, a(n) for n = 1..65537

Index entries for sequences related to binary expansion of n

Index entries for sequences related to sigma(n)

Formula

a(n) = A004198(n, A001065(n)).

a(n) = A000203(n) - A318456(n) = (A000203(n)-A318457(n))/2.

Mathematica

Table[BitAnd[n, DivisorSigma[1, n] - n], {n, 100}] (* Vincenzo Librandi, Aug 29 2018 *)

Prog

(PARI) A318458(n) = bitand(n, sigma(n)-n);
(Magma) [SumOfDivisors(n)-BitwiseOr(n, SumOfDivisors(n)-n): n in [1..100]]; // Vincenzo Librandi, Aug 29 2018

Crossrefs

Cf. A000203, A001065, A004198, A033879, A318456, A318457.

Cf. also A318468, A318508, A318518, A318463.

Sequence in context: A059117 A340206 A196603 * A267479 A285824 A269955

Adjacent sequences: A318455 A318456 A318457 * A318459 A318460 A318461

Keyword

nonn,base,look

Author

Antti Karttunen, Aug 26 2018

Status

approved