A294903 Number of divisors of n that are in A257691.

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

Offset

1,2

Comments

Number of terms of A257691 that divide n.

Links

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

Formula

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

a(n) = A294901(n) + A294905(n).

a(n) + A294904(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));
A294903(n) = sumdiv(n, d, A294905(d));

Crossrefs

Cf. A000120, A257691, A292257, A294901, A294902, A294904, A294905.

Cf. also A294893.

Sequence in context: A287841 A083399 A105561 * A087133 A324292 A196941

Adjacent sequences: A294900 A294901 A294902 * A294904 A294905 A294906

Keyword

nonn,base

Author

Antti Karttunen, Nov 10 2017

Status

approved