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Revision History for A305614

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Showing entries 1-10 | older changes

A305614

Expansion of Sum_{p prime} x^p/(1 + x^p).
(history; published version)

#20 by Bruno Berselli at Wed Aug 01 10:31:59 EDT 2018

STATUS

proposed

approved

#19 by Ilya Gutkovskiy at Mon Jul 30 15:17:45 EDT 2018

STATUS

editing

proposed

#18 by Ilya Gutkovskiy at Mon Jul 30 14:13:47 EDT 2018

FORMULA

L.g.f.: log(Product_{k>=1} (1 + x^prime(k))^(1/prime(k))) = Sum_{n>=1} a(n)*x^n/n. - Ilya Gutkovskiy, Jul 30 2018

STATUS

approved

editing

#17 by Alois P. Heinz at Thu Jun 07 18:17:27 EDT 2018

STATUS

proposed

approved

#16 by Robert Israel at Thu Jun 07 18:00:34 EDT 2018

STATUS

editing

proposed

#15 by Robert Israel at Thu Jun 07 18:00:24 EDT 2018

FORMULA

From Robert Israel, Jun 07 2018: (Start)

If n is odd, a(n) = A001221(n).

If n == 2 (mod 4), a(n) = 2 - A001221(n).

If n == 0 (mod 4) and n > 0, a(n) = -A001221(n). (End)

#14 by Robert Israel at Thu Jun 07 17:47:55 EDT 2018

LINKS

Robert Israel, <a href="/A305614/b305614.txt">Table of n, a(n) for n = 0..10000</a>

MAPLE

# Alternative

N:= 1000: # to get a(0)..a(N)

V:= Vector(N):

p:= 1:

do

p:= nextprime(p);

if p > N then break fi;

R:= [seq(i, i=p..N, p)];

W:= <seq((-1)^(n+1), n=1..nops(R))>;

V[R]:= V[R]+W;

od:

[0, seq(V[i], i=1..N)]; # Robert Israel, Jun 07 2018

STATUS

approved

editing

#13 by Alois P. Heinz at Thu Jun 07 14:23:14 EDT 2018

STATUS

proposed

approved

#12 by Alois P. Heinz at Thu Jun 07 11:08:44 EDT 2018

STATUS

editing

proposed

#11 by Alois P. Heinz at Thu Jun 07 11:07:29 EDT 2018

MAPLE

a:= n-> -add((-1)^(n/i[1]), i=ifactors(n)[2]):

seq(a(n), n=0..100); # Alois P. Heinz, Jun 07 2018

STATUS

proposed

editing