The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A284943

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A284943

Expansion of Sum_{p prime, k>=1} x^(p^k)*(1 - x)^2/(1 - 2*x)^2.
(history; published version)

#15 by Alois P. Heinz at Wed Aug 07 17:17:49 EDT 2019

STATUS

editing

approved

#14 by Alois P. Heinz at Wed Aug 07 17:17:46 EDT 2019

LINKS

Alois P. Heinz, <a href="/A284943/b284943.txt">Table of n, a(n) for n = 1..3313</a>

#13 by Alois P. Heinz at Wed Aug 07 17:14:02 EDT 2019

MAPLE

b:= proc(n) option remember; nops(ifactors(n)[2])=1 end:

a:= proc(n) option remember; `if`(n=0, 0, add(a(n-j)+

`if`(b(j), ceil(2^(n-j-1)), 0), j=1..n))

end:

seq(a(n), n=1..33); # Alois P. Heinz, Aug 07 2019

STATUS

approved

editing

#12 by N. J. A. Sloane at Thu Apr 06 21:11:42 EDT 2017

STATUS

proposed

approved

#11 by Indranil Ghosh at Thu Apr 06 14:37:23 EDT 2017

STATUS

editing

proposed

#10 by Indranil Ghosh at Thu Apr 06 14:36:53 EDT 2017

PROG

(PARI) x='x+O('x^34); concat([0], Vec(sum(k=2, 34, (1\omega(k))*x^k*(1 - x)^2/(1 - 2*x)^2))) \\ Indranil Ghosh, Apr 06 2017

STATUS

proposed

editing

#9 by Ilya Gutkovskiy at Thu Apr 06 11:27:13 EDT 2017

STATUS

editing

proposed

#8 by Ilya Gutkovskiy at Thu Apr 06 11:26:09 EDT 2017

MATHEMATICA

nmax = 33; Rest[CoefficientList[Series[Sum[Floor[1/PrimeNu[k]] x^k (1 - x)^2/(1 - 2 x)^2, {k, 2, 2 nmax}], {x, 0, nmax}], x]]

#7 by Ilya Gutkovskiy at Thu Apr 06 10:17:20 EDT 2017

MATHEMATICA

nmax = 33; Rest[CoefficientList[Series[Sum[Floor[1/PrimeNu[k]] x^k (1 - x)^2/(1 - 2 x)^2, {k, 2, 2 nmax}], {x, 0, nmax}], x]]

STATUS

proposed

editing

#6 by Ilya Gutkovskiy at Thu Apr 06 10:02:51 EDT 2017

STATUS

editing

proposed