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A120271
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Numerator of Sum[ 1/(Prime[k]-1), {k,1,n}].
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7
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1, 3, 7, 23, 121, 21, 173, 1597, 17927, 127469, 129317, 43619, 44081, 44521, 1033223, 13538159, 395369371, 132680013, 400467919, 402757063, 1214947859, 1221110939, 50305908619, 50529880549, 101470376303, 509322834499, 8691337402883
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| a(n) are squarefree except for n=5,14,49,.. where squared prime factors are 11,211,479,...
a(n) divides A078456(n) = {1, 3, 14, 92, 968, 12096, 199296, 3679488, ...} = Number of numbers less than p(1)*p(2)*...*p(n) having exactly one prime factor among (p(1),p(2)....,p(n)) where p(n) is the n-th prime. The quotients are A078456(n)/a(n) = A135212(n) = {1, 1, 2, 4, 8, 576, 1152, 2304, 4608, 18432, 552960, ...}. - Alexander Adamchuk (alex(AT)kolmogorov.com), Nov 23 2007
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LINKS
| Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics. Prime Sums.
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FORMULA
| a(n) = numerator[ Sum[ 1/(Prime[k]-1), {k,1,n}]].
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MATHEMATICA
| Numerator[Table[Sum[1/(Prime[i]-1), {i, 1, n}], {n, 1, 50}]]
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CROSSREFS
| Cf. A119686, A006093, A000040.
Cf. A135212, A078456.
Sequence in context: A080077 A096318 A133788 * A145938 A048721 A113824
Adjacent sequences: A120268 A120269 A120270 * A120272 A120273 A120274
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KEYWORD
| frac,nonn
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AUTHOR
| Alexander Adamchuk (alex(AT)kolmogorov.com), Jul 01 2006
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