OFFSET
1,3
COMMENTS
Number of ways to write n as a sum a_1 + ... + a_k where the a_i are positive integers and a_i = 2 * a_{i-1}, cf. A000929.
Number of divisors of n of the form 2^k - 1 (A000225) for k >= 1. - Jeffrey Shallit, Jan 23 2017
LINKS
Antti Karttunen, Table of n, a(n) for n = 1..65537 (first 10000 terms from Robert Israel)
FORMULA
G.f.: Sum_{k>0} x^(2^k-1)/(1-x^(2^k-1)).
From Antti Karttunen, Jun 11 2018: (Start)
a(n) = Sum_{d|n} A036987(d).
Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = A065442 = 1.606695... . - Amiram Eldar, Dec 31 2023
MAPLE
N:= 200: # to get a(1)..a(N)
A:= Vector(N):
for k from 1 do
t:= 2^k-1;
if t > N then break fi;
R:= [seq(i, i=t..N, t)];
A[R]:= map(`+`, A[R], 1)
od:
convert(A, list); # Robert Israel, Jan 23 2017
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));
(PARI) A154402(n) = { my(m=1, s=0); while(m<=n, s += !(n%m); m += (m+1)); (s); }; \\ Antti Karttunen, May 12 2022
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Vladeta Jovovic, Jan 08 2009
STATUS
approved