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A305436
Number of divisors of n of the form 2^k + 1 for k >= 0.
5
0, 1, 1, 1, 1, 2, 0, 1, 2, 2, 0, 2, 0, 1, 2, 1, 1, 3, 0, 2, 1, 1, 0, 2, 1, 1, 2, 1, 0, 3, 0, 1, 2, 2, 1, 3, 0, 1, 1, 2, 0, 2, 0, 1, 3, 1, 0, 2, 0, 2, 2, 1, 0, 3, 1, 1, 1, 1, 0, 3, 0, 1, 2, 1, 2, 3, 0, 2, 1, 2, 0, 3, 0, 1, 2, 1, 0, 2, 0, 2, 2, 1, 0, 2, 2, 1, 1, 1, 0, 4, 0, 1, 1, 1, 1, 2, 0, 1, 3, 2, 0, 3, 0, 1, 2
OFFSET
1,6
COMMENTS
a(n) is the number of terms of A000051 that divide n.
LINKS
FORMULA
a(n) = Sum_{d|n} A209229(d-1).
a(n) = A305435(n) + A209229(n-1).
Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = A323482 = 1.264499... . - Amiram Eldar, Dec 31 2023
MATHEMATICA
Table[DivisorSum[n, 1 &, IntegerQ@ Log2[# - 1] &], {n, 105}] (* Michael De Vlieger, Jun 11 2018 *)
PROG
(PARI)
A209229(n) = (n && !bitand(n, n-1));
A305436(n) = sumdiv(n, d, A209229(d-1));
CROSSREFS
Cf. A000051, A209229, A292315 (positions of zeros), A305435, A323482.
Cf. also A154402.
Sequence in context: A354786 A147767 A113678 * A328708 A299480 A110249
KEYWORD
nonn
AUTHOR
Antti Karttunen, Jun 11 2018
STATUS
approved