A294902 Number of proper divisors of n that are in A175526.

0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 2, 0, 2, 0, 2, 0, 0, 0, 4, 0, 0, 1, 2, 0, 3, 0, 3, 0, 0, 0, 5, 0, 0, 0, 4, 0, 3, 0, 2, 2, 0, 0, 6, 0, 1, 0, 2, 0, 4, 0, 4, 0, 0, 0, 7, 0, 0, 2, 4, 0, 3, 0, 2, 0, 3, 0, 8, 0, 0, 1, 2, 0, 3, 0, 6, 2, 0, 0, 7, 0, 0, 0, 4, 0, 7, 0, 2, 0, 0, 0, 8, 0, 2, 2, 4, 0, 3, 0, 4, 3, 0, 0, 8, 0, 3, 0, 6, 0, 3, 0, 2, 2, 0, 0, 11

Offset

1,12

Links

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

Formula

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

a(n) = A294904(n) + A294905(n) - 1.

a(n) + A294901(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));
A294902(n) = sumdiv(n, d, (d<n)*(0==A294905(d)));

Crossrefs

Cf. A000120, A032741, A175526, A292257, A294901, A294903, A294904, A294905.

Cf. also A294892.

Sequence in context: A112313 A297115 A337346 * A321516 A172246 A087893

Adjacent sequences: A294899 A294900 A294901 * A294903 A294904 A294905

Keyword

nonn,base

Author

Antti Karttunen, Nov 10 2017

Status

approved