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 A154402 Inverse Moebius transform of Fredholm-Rueppel sequence, cf. A036987. 7
 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) 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 CROSSREFS Cf. A000225, A001511, A036987, A161790 (positions of 1's), A305426. Cf. also A305436. Sequence in context: A060236 A006345 A122497 * 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 January 21 05:39 EST 2020. Contains 331104 sequences. (Running on oeis4.)