

A006520


Partial sums of A006519.
(Formerly M2344)


6



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

1,2


COMMENTS

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]


REFERENCES

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).


LINKS

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 divideandconquer sequences ...
Ralf Stephan, Table of generating functions


FORMULA

a(n)/(n*log(n)) is bounded.  Benoit Cloitre, Dec 17 2002
G.f.: 1/x/(1x) * (x/(1x) + Sum(k>=1, 2^(k1)*x^2^k/(1x^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^k1) = k*2^(k1) = A001787(k) for any k > 0.  Rémy Sigrist, Jan 21 2021


MATHEMATICA

Table[ 2^IntegerExponent[n, 2], {n, 1, 70}] // Accumulate (* JeanFrançois Alcover, May 14 2013 *)


PROG

(PARI) a(n)=sum(i=1, n, 2^valuation(i, 2))


CROSSREFS

First differences of A022560.
Cf. A001787.
Sequence in context: A047460 A193532 A068056 * A054204 A050003 A002156
Adjacent sequences: A006517 A006518 A006519 * A006521 A006522 A006523


KEYWORD

nonn,easy


AUTHOR

N. J. A. Sloane, Simon Plouffe


EXTENSIONS

More terms from Benoit Cloitre, Dec 17 2002
Offset changed to 1 by N. J. A. Sloane, Oct 18 2019


STATUS

approved



