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 A154402 Inverse Moebius transform of Fredholm-Rueppel sequence, cf. A036987. 42
 1, 1, 2, 1, 1, 2, 2, 1, 2, 1, 1, 2, 1, 2, 3, 1, 1, 2, 1, 1, 3, 1, 1, 2, 1, 1, 2, 2, 1, 3, 2, 1, 2, 1, 2, 2, 1, 1, 2, 1, 1, 3, 1, 1, 3, 1, 1, 2, 2, 1, 2, 1, 1, 2, 1, 2, 2, 1, 1, 3, 1, 2, 4, 1, 1, 2, 1, 1, 2, 2, 1, 2, 1, 1, 3, 1, 2, 2, 1, 1, 2, 1, 1, 3, 1, 1, 2, 1, 1, 3, 2, 1, 3, 1, 1, 2, 1, 2, 2, 1, 1, 2, 1, 1, 4 (list; graph; refs; listen; history; text; internal format)
 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). a(n) = A305426(n) + A036987(n). (End) a(n) = A147645(n) + A353786(n). - Antti Karttunen, May 12 2022 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)); A036987(n) = A209229(1+n); A154402(n) = sumdiv(n, d, A036987(d)); \\ Antti Karttunen, Jun 11 2018 (PARI) A154402(n) = { my(m=1, s=0); while(m<=n, s += !(n%m); m += (m+1)); (s); }; \\ Antti Karttunen, May 12 2022 CROSSREFS Cf. A000225, A001511, A036987, A147645, A161790 (positions of 1's), A305426, A353786. Cf. also A305436. Sequence in context: A006345 A122497 A350330 * A210682 A293433 A177025 Adjacent sequences:  A154399 A154400 A154401 * A154403 A154404 A154405 KEYWORD easy,nonn AUTHOR Vladeta Jovovic, Jan 08 2009 STATUS approved

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Last modified June 29 07:33 EDT 2022. Contains 354910 sequences. (Running on oeis4.)