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A268235 a(n) = Sum_{k=1..n} floor(n/k)*2^(k-1). 1
1, 4, 9, 20, 37, 76, 141, 280, 541, 1072, 2097, 4192, 8289, 16548, 32953, 65860, 131397, 262764, 524909, 1049736, 2098381, 4196560, 8390865, 16781696, 33558929, 67117460, 134226585, 268452580, 536888037, 1073775900, 2147517725, 4295034280, 8590002605, 17180002736, 34359872001, 68719743792 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

This is the "floor transform" of the powers of 2.

LINKS

Matthew House, Table of n, a(n) for n = 1..3305

MAPLE

# floor transform of a sequence

ft:=proc(a) local b, n, j, k; b:=[];

for n from 1 to nops(a) do j:=add(a[k]*floor(n/k), k=1..n); b:=[op(b), j]; od;

b; end:

ft([seq(2^i, i=0..50)]);

MATHEMATICA

Table[Sum[Floor[n/k] 2^(k - 1), {k, n}], {n, 36}] (* Michael De Vlieger, Feb 12 2017 *)

PROG

(PARI) a(n) = sum(k=1, n, (n\k)*2^(k-1)); \\ Michel Marcus, Feb 11 2017

CROSSREFS

First differences give A034729. Cf. A000079.

Sequence in context: A009910 A060494 A049748 * A192956 A023607 A117074

Adjacent sequences:  A268232 A268233 A268234 * A268236 A268237 A268238

KEYWORD

nonn

AUTHOR

Benoit Cloitre and N. J. A. Sloane, Feb 05 2016

EXTENSIONS

Definition corrected by Matthew House, Feb 11 2017

STATUS

approved

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Last modified October 18 05:18 EDT 2019. Contains 328146 sequences. (Running on oeis4.)