A292257 a(n) is the total number of 1's in binary expansion of all proper divisors of n.

0, 1, 1, 2, 1, 4, 1, 3, 3, 4, 1, 7, 1, 5, 5, 4, 1, 8, 1, 7, 6, 5, 1, 10, 3, 5, 5, 9, 1, 14, 1, 5, 6, 4, 6, 13, 1, 5, 6, 10, 1, 15, 1, 9, 11, 6, 1, 13, 4, 9, 5, 9, 1, 14, 6, 13, 6, 6, 1, 23, 1, 7, 11, 6, 6, 14, 1, 7, 7, 15, 1, 18, 1, 5, 12, 9, 7, 16, 1, 13, 9, 5, 1, 24, 5, 6, 7, 13, 1, 26, 7, 11, 8, 7, 6, 16, 1, 11, 10, 15, 1, 14, 1, 13, 18

Offset: 1

Author

Antti Karttunen, Oct 04 2017

Keywords

• nonn
• base

Comments

If a(n) == A000120(n), then n is in A175522, if a(n) < A000120(n), then n is in A175524, and if a(n) > A000120(n), then n is in A175526.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384
• Index entries for sequences related to binary expansion of n.

Crossrefs

Cf. A000120, A093653, A175522, A175524, A175526, A192895, A290090, A293214.

Programs

Mathematica

a[n_] := DivisorSum[n, DigitCount[#, 2, 1] &, # < n &]; Array[a, 100] (* Amiram Eldar, Jul 20 2023 *)
Table[Total[Flatten[IntegerDigits[#,2]&/@Most[Divisors[n]]]],{n,120}] (* Harvey P. Dale, Oct 11 2024 *)

PARI

A292257(n) = sumdiv(n,d,(d
				

Formula

a(n) = Sum_{d|n, dA000120(d).

a(n) = A093653(n) - A000120(n).

a(n) = A192895(n) + A000120(n).

a(n) = A001222(A293214(n)).

A000035(a(n)) = A000035(A290090(n)). [Parity-wise equivalent with A290090.]