A331970 The sum of the proper bi-unitary divisors of n.

0, 1, 1, 1, 1, 6, 1, 7, 1, 8, 1, 8, 1, 10, 9, 11, 1, 12, 1, 10, 11, 14, 1, 36, 1, 16, 13, 12, 1, 42, 1, 31, 15, 20, 13, 14, 1, 22, 17, 50, 1, 54, 1, 16, 15, 26, 1, 60, 1, 28, 21, 18, 1, 66, 17, 64, 23, 32, 1, 60, 1, 34, 17, 55, 19, 78, 1, 22, 27, 74, 1, 78, 1

Offset

1,6

Comments

First differs from A126168 at n = 16.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Formula

a(n) = A188999(n) - n.

Example

a(6) = 6 since A188999(6) - 6 = 12 - 6 = 6.

Mathematica

fun[p_, e_] := If[OddQ[e], (p^(e+1)-1)/(p-1), (p^(e+1)-1)/(p-1)-p^(e/2)]; bsigma[1] = 1; bsigma[n_] := bsigma[n] = Times @@ (fun @@@ FactorInteger[n]); bs[n_] := bsigma[n] - n; Array[bs, 100]

Crossrefs

Cf. A001065, A034460, A126164, A126168, A188999, A222266.

Sequence in context: A299620 A113811 A126168 * A028323 A137235 A021166

Adjacent sequences: A331967 A331968 A331969 * A331971 A331972 A331973

Keyword

nonn

Author

Amiram Eldar, Feb 03 2020

Status

approved