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

Author

Antti Karttunen, Aug 26 2018

Keywords

• nonn
• base
• look

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)

Crossrefs

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

Cf. also A318468, A318508, A318518, A318463.

Programs

Magma

[SumOfDivisors(n)-BitwiseOr(n, SumOfDivisors(n)-n): n in [1..100]]; // Vincenzo Librandi, Aug 29 2018

Mathematica

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

PARI

A318458(n) = bitand(n,sigma(n)-n);

Formula

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

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