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Search: id:A128649
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| A128649 |
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a(n) = numbers n such that denominator of Sum[ 1/(Prime[k]-1), {k,1,n} ] equals denominator of Sum[ (-1)^(k+1)*1/(Prime[k]-1), {k,1,n} ]; or A128646(n) = A128648(n). |
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4
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| 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, 72, 73, 74, 75, 76, 77, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 539, 540, 541, 542, 543, 600, 601, 602, 603, 604, 605, 606, 607, 608, 609, 610
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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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} ]. A128646(n) = {1,2,4,12,60,10,80,720,7920,55440,55440,18480,18480,18480,...} = Denominator of Sum[ 1/(Prime[k]-1), {k,1,n} ]. Numbers n such that A128648(n) equals A128646(n) are 1-5,7-11,14-17,21-35,65-66,71-77,81-93,539-543,600-639,644-650,707-818,1152-1185,4502-4577,4601-4823,4893-5003,7483-7633,...
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LINKS
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Eric Weisstein, Link to a section of The World of Mathematics. Prime Sums.
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FORMULA
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A128646(n) = A128648(n).
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MATHEMATICA
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f=0; g=0; Do[p=Prime[n]; f=f+1/(p-1); g=g+(-1)^(n+1)*1/(p-1); kf=Denominator[f]; kg=Denominator[g]; If[Equal[kf, kg], Print[n]], {n, 1, 10000}]
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CROSSREFS
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Cf. A128648 = Denominator of Sum[ (-1)^(k+1)*1/(Prime[k]-1), {k, 1, n} ]. Cf. A128646 = Denominator of Sum[ 1/(Prime[k]-1), {k, 1, n} ]. Cf. A128647, A120271, A119686, A006093, A000040.
Sequence in context: A055019 A014122 A004764 this_sequence A032894 A032853 A023748
Adjacent sequences: A128646 A128647 A128648 this_sequence A128650 A128651 A128652
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KEYWORD
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nonn
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AUTHOR
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Alexander Adamchuk (alex(AT)kolmogorov.com), Mar 18 2007
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