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A006520
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Partial sums of A006519.
(Formerly M2344)
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6
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1, 3, 4, 8, 9, 11, 12, 20, 21, 23, 24, 28, 29, 31, 32, 48, 49, 51, 52, 56, 57, 59, 60, 68, 69, 71, 72, 76, 77, 79, 80, 112, 113, 115, 116, 120, 121, 123, 124, 132, 133, 135, 136, 140, 141, 143, 144, 160, 161, 163, 164, 168, 169, 171, 172, 180, 181, 183, 184, 188, 189
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OFFSET
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1,2
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COMMENTS
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The subsequence of primes in this partial sum begins: 3, 11, 23, 29, 31, 59, 71, 79, 113, 163, 181. The subsequence of powers in this partial sum begins: 1, 4, 8, 9, 32, 49, 121, 144, 169. [Jonathan Vos Post, Feb 18 2010]
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 1..1001 [Jul 23 2013; offset adapted by Georg Fischer, Jan 27 2020]
V. Meally, Letter to N. J. A. Sloane, May 1975
Ralf Stephan, Some divide-and-conquer sequences ...
Ralf Stephan, Table of generating functions
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FORMULA
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a(n)/(n*log(n)) is bounded. - Benoit Cloitre, Dec 17 2002
G.f.: 1/x/(1-x) * (x/(1-x) + Sum(k>=1, 2^(k-1)*x^2^k/(1-x^2^k))). - Ralf Stephan, Apr 17 2003
a(n) = b(n+1), with b(2n) = 2b(n) + n, b(2n+1) = 2b(n) + n + 1. - Ralf Stephan, Sep 07 2003
a(2^k-1) = k*2^(k-1) = A001787(k) for any k > 0. - Rémy Sigrist, Jan 21 2021
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MATHEMATICA
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Table[ 2^IntegerExponent[n, 2], {n, 1, 70}] // Accumulate (* Jean-François Alcover, May 14 2013 *)
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PROG
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(PARI) a(n)=sum(i=1, n, 2^valuation(i, 2))
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CROSSREFS
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First differences of A022560.
Cf. A001787.
Sequence in context: A047460 A193532 A068056 * A054204 A050003 A002156
Adjacent sequences: A006517 A006518 A006519 * A006521 A006522 A006523
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane, Simon Plouffe
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EXTENSIONS
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More terms from Benoit Cloitre, Dec 17 2002
Offset changed to 1 by N. J. A. Sloane, Oct 18 2019
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STATUS
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approved
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