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

1,4

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.

Formula

a(n) = Sum_{d|n, d<n} A000120(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.]

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 *)

Prog

(PARI) A292257(n) = sumdiv(n, d, (d<n)*hammingweight(d));

Crossrefs

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

Sequence in context: A088372 A331601 A243504 * A317837 A296074 A239451

Adjacent sequences: A292254 A292255 A292256 * A292258 A292259 A292260

Keyword

nonn,base

Author

Antti Karttunen, Oct 04 2017

Status

approved