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Search: id:A076265
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| A076265 |
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Product_{ i=1..n } prime(i)^prime(i). |
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+0
10
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| 4, 108, 337500, 277945762500, 79301169838123235887500, 24018350267611933650627567399079537500, 19868946365457062696924774946056904675112420776003728137500
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Denominator of Sum[i=1..n] 1/(p(i)^p(i)), where p(i) = i-th prime. Numerators = A117579. E.g. 1/4, 31/108, 96983/337500, 79870008269/277945762500, 22787845491220720044859/79301169838123235887500, ... - Jonathan Vos Post (jvospost3(AT)gmail.com), Mar 29 2006
Equally, denominator of Sum[ (-1)^(k+1) * 1/p(k)^p(k), {k,1,n}], where p(k) = Prime[k]. - Alexander Adamchuk (alex(AT)kolmogorov.com), Aug 22 2006
C = Sum[ (-1)^(k+1) * 1/Prime[k]^Prime[k], {k,1,Infinity} ] = 1/2^2 - 1/3^3 + 1/5^5 - 1/7^7 + 1/11^11 - 1/13^13 + ... A122147[n] is a decimal expansion of C = 0.213281748700785698255627... - Alexander Adamchuk (alex(AT)kolmogorov.com), Aug 22 2006
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EXAMPLE
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A122148[n] / A076265[n] begins 1/4, 23/108, 71983/337500, ... - Alexander Adamchuk (alex(AT)kolmogorov.com), Aug 22 2006
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MATHEMATICA
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Table[Denominator[Sum[1/Prime[k]^Prime[k], {k, 1, n}]], {n, 1, 10}] - Alexander Adamchuk (alex(AT)kolmogorov.com), Aug 22 2006
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CROSSREFS
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Cf. A051674, A122147, A122148, A094289, A117579, A076265, A000040.
Sequence in context: A061464 A107048 A002109 this_sequence A114876 A037980 A015100
Adjacent sequences: A076262 A076263 A076264 this_sequence A076266 A076267 A076268
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KEYWORD
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nonn,frac
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AUTHOR
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Jeff Burch (gburch(AT)erols.com), Nov 23 2002
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EXTENSIONS
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Entry revised by N. J. A. Sloane (njas(AT)research.att.com), Apr 10 2006
Edited by N. J. A. Sloane (njas(AT)research.att.com), Aug 04 2008 at the suggestion of R. J. Mathar
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