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A154402 Inverse Moebius transform of Fredholm-Rueppel sequence, cf. A036987. 6
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

From Antti Karttunen, Jun 11 2018: (Start)

a(n) = Sum_{d|n} A036987(d).

a(n) = A305426(n) + A036987(n).

(End)

EXAMPLE

G.f.: Sum_{k>0} x^(2^k-1)/(1-x^(2^k-1)).

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 November 19 05:29 EST 2018. Contains 317333 sequences. (Running on oeis4.)