A294901 Number of proper divisors of n that are in A257691.

0, 1, 1, 2, 1, 3, 1, 2, 2, 3, 1, 3, 1, 3, 3, 2, 1, 3, 1, 3, 3, 3, 1, 3, 2, 3, 2, 3, 1, 4, 1, 2, 3, 3, 3, 3, 1, 3, 3, 3, 1, 4, 1, 3, 3, 3, 1, 3, 2, 4, 3, 3, 1, 3, 3, 3, 3, 3, 1, 4, 1, 3, 3, 2, 3, 4, 1, 3, 3, 4, 1, 3, 1, 3, 4, 3, 3, 4, 1, 3, 2, 3, 1, 4, 3, 3, 3, 3, 1, 4, 3, 3, 3, 3, 3, 3, 1, 3, 3, 4, 1, 4, 1, 3, 4, 3, 1, 3, 1, 4, 3, 3, 1, 4, 3, 3, 3, 3, 3, 4

Offset

1,4

Links

Antti Karttunen, Table of n, a(n) for n = 1..25000

Formula

a(n) = Sum_{d|n, d<n} A294905(d).

a(n) = A294903(n) - A294905(n).

a(n) + A294902(n) = A032741(n).

Mathematica

q[n_] := DivisorSum[n, DigitCount[#, 2, 1] &] <= 2*DigitCount[n, 2, 1]; a[n_] := DivisorSum[n, 1 &, # < n && q[#] &]; Array[a, 100] (* Amiram Eldar, Jul 20 2023 *)

Prog

(PARI)
A292257(n) = sumdiv(n, d, (d<n)*hammingweight(d));
A294905(n) = (A292257(n) <= hammingweight(n));
A294901(n) = sumdiv(n, d, (d<n)*A294905(d));

Crossrefs

Cf. A000120, A032741, A257691, A292257, A294902, A294903, A294904, A294905.

Cf. also A294891.

Sequence in context: A353646 A154263 A293435 * A347042 A333416 A305818

Adjacent sequences: A294898 A294899 A294900 * A294902 A294903 A294904

Keyword

nonn,base

Author

Antti Karttunen, Nov 10 2017

Status

approved