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A128647 Numerator of Sum[ (-1)^(k+1)*1/(Prime[k]-1), {k,1,n} ]. 3
1, 1, 3, 7, 41, 3, 53, 437, 5167, 34189, 36037, 3833, 3987, 11521, 274223, 3458639, 103063291, 100392623, 34273501, 33510453, 308270747, 302107667, 12626774467, 12402802537, 25216220279, 124110148411, 2142721739387, 111888942151111 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

A128648(n) = {1,2,4,12,60,5,80,720,7920,55440,55440,6160,6160,18480,...} = Denominator of Sum[ (-1)^(k+1)*1/(Prime[k]-1), {k,1,n} ]. A120271(n) = {1,3,7,23,121,21,173,1597,17927,127469,129317,43619,...} = Numerator of Sum[ 1/(Prime[k]-1), {k,1,n} ]. Numbers n such that A128648(n) equals A128646(n) are listed in A128649(n) = {1,2,3,4,5,7,8,9,10,11,14,15,16,17,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,65,66,71,...}.

LINKS

Table of n, a(n) for n=1..28.

Eric Weisstein's World of Mathematics, Prime sums

FORMULA

a(n) = Numerator[ Sum[ (-1)^(k+1)*1/(Prime[k]-1), {k,1,n} ] ].

MATHEMATICA

Table[Numerator[Sum[(-1)^(k+1)*1/(Prime[k]-1), {k, 1, n}]], {n, 1, 36}]

CROSSREFS

Cf. A128648 = Denominator of Sum[ (-1)^(k+1)*1/(Prime[k]-1), {k, 1, n} ]. Cf. A120271 = Numerator of Sum[ 1/(Prime[k]-1), {k, 1, n} ]. Cf. A128646, A128649, A119686, A006093, A000040.

Sequence in context: A019024 A135071 A096219 * A071730 A058815 A333649

Adjacent sequences:  A128644 A128645 A128646 * A128648 A128649 A128650

KEYWORD

frac,nonn

AUTHOR

Alexander Adamchuk, Mar 18 2007

STATUS

approved

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Last modified August 9 02:14 EDT 2020. Contains 336310 sequences. (Running on oeis4.)