A294904 Number of divisors of n that are in A175526.

0, 0, 0, 1, 0, 1, 0, 2, 1, 1, 0, 3, 0, 1, 1, 3, 0, 3, 0, 3, 1, 1, 0, 5, 0, 1, 2, 3, 0, 4, 0, 4, 1, 1, 1, 6, 0, 1, 1, 5, 0, 4, 0, 3, 3, 1, 0, 7, 1, 2, 1, 3, 0, 5, 1, 5, 1, 1, 0, 8, 0, 1, 3, 5, 1, 4, 0, 3, 1, 4, 0, 9, 0, 1, 2, 3, 1, 4, 0, 7, 3, 1, 0, 8, 1, 1, 1, 5, 0, 8, 1, 3, 1, 1, 0, 9, 0, 3, 3, 5, 0, 4, 0, 5, 4, 1, 0, 9, 0, 4, 0, 7, 0, 4, 1, 3, 3, 1, 0, 12

Offset

1,8

Comments

Number of terms of A175526 that divide n.

Links

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

Formula

a(n) = Sum_{d|n} (1-A294905(d)).

a(n) = 1 + (A294902(n)-A294905(n)).

a(n) + A294903(n) = A000005(n).

Mathematica

q[n_] := DivisorSum[n, DigitCount[#, 2, 1] &] > 2 * DigitCount[n, 2, 1]; a[n_] := DivisorSum[n, 1 &, 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));
A294904(n) = sumdiv(n, d, (0==A294905(d)));

Crossrefs

Cf. A000120, A175526, A292257, A294901, A294902, A294903, A294905.

Cf. also A294894.

Sequence in context: A114206 A073202 A337345 * A055212 A360661 A028422

Adjacent sequences: A294901 A294902 A294903 * A294905 A294906 A294907

Keyword

nonn,base

Author

Antti Karttunen, Nov 10 2017

Status

approved