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A029930 If 2n = Sum 2^e_i, a(n) = Product 2^e_i. 7
1, 2, 4, 8, 8, 16, 32, 64, 16, 32, 64, 128, 128, 256, 512, 1024, 32, 64, 128, 256, 256, 512, 1024, 2048, 512, 1024, 2048, 4096, 4096, 8192, 16384, 32768, 64, 128, 256, 512, 512, 1024, 2048, 4096, 1024, 2048, 4096, 8192, 8192, 16384, 32768, 65536, 2048 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..1000

Arvind Ayyer, A. Prasad, S. Spallone, Representations of symmetric groups with non-trivial determinant, arXiv preprint arXiv:1604.08837 [math.RT], 2016. See Eq. (14).

FORMULA

From Ralf Stephan, Jun 19 2003: (Start)

G.f.: Prod_{k>=0} 1+2^(k+1)x^2^k.

a(0) = 1, a(2n) = 2^e1(n)*a(n), a(2n+1) = 2a(2n), where e1(n) = A000120(n).

a(n) = 2^A029931(n). (End)

EXAMPLE

14 = 8+4+2 so a(7) = 8*4*2 = 64.

MATHEMATICA

e1[n_] := Total[IntegerDigits[n, 2]]; a[0] = 1; a[n_] := a[n] = If[EvenQ[ n], 2^e1[n/2] a[n/2], 2 a[n-1]]; Table[a[n], {n, 0, 50}] (* Jean-Fran├žois Alcover, Mar 07 2016 *)

PROG

(PARI) a(n) = {my(bd = Vecrev(binary(n))); prod(k=1, #bd, if (bd[k], 2^k, 1)); } \\ Michel Marcus, Mar 07 2016

CROSSREFS

Cf. A000120, A029931, A073642.

A bisection of A059867.

Sequence in context: A076735 A192097 A132720 * A193850 A140119 A273068

Adjacent sequences:  A029927 A029928 A029929 * A029931 A029932 A029933

KEYWORD

nonn,easy,look

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified March 29 17:23 EDT 2020. Contains 333116 sequences. (Running on oeis4.)