login
A292257
a(n) is the total number of 1's in binary expansion of all proper divisors of n.
16
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.
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));
KEYWORD
nonn,base
AUTHOR
Antti Karttunen, Oct 04 2017
STATUS
approved