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 A076265 a(n) = Product_{i=1..n} prime(i)^prime(i). 9
 4, 108, 337500, 277945762500, 79301169838123235887500, 24018350267611933650627567399079537500, 19868946365457062696924774946056904675112420776003728137500 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Denominator of Sum_{i=1..n} 1/(p(i)^p(i)), where p(i) = i-th prime. The numerators are in A117579. E.g., 1/4, 31/108, 96983/337500, 79870008269/277945762500, ... - Jonathan Vos Post, Mar 29 2006 Equally, denominator of Sum_{k=1..n}(-1)^(k+1) * 1/p(k)^p(k), where p(k) = prime(k). - Alexander Adamchuk, Aug 22 2006 C = Sum_{k>=1}(-1)^(k+1) * 1/prime(k)^prime(k)) = 1/2^2 - 1/3^3 + 1/5^5 - 1/7^7 + 1/11^11 - 1/13^13 + ... A122147 is the decimal expansion of C = 0.213281748700785698255627... - Alexander Adamchuk, Aug 22 2006 Hyperprimorials, from primorials by analogy with hyperfactorials. See A006939. - Matthew Campbell, Jul 30 2015 LINKS FORMULA log a(n) ~ (n^2 log^2 n)/2. - Charles R Greathouse IV, Sep 14 2015 EXAMPLE A122148(n)/a(n) begins 1/4, 23/108, 71983/337500, ... - Alexander Adamchuk, Aug 22 2006 MATHEMATICA Table[Denominator[Sum[1/Prime[k]^Prime[k], {k, 1, n}]], {n, 1, 10}] (* Alexander Adamchuk, Aug 22 2006 *) Denominator[Accumulate[1/#^#&/@Prime[Range[10]]]] (* Harvey P. Dale, Jan 24 2013 *) PROG (PARI) a(n)=prod(i=1, n, prime(i)^prime(i)) \\ Charles R Greathouse IV, Aug 05 2015 CROSSREFS Cf. A051674, A122147, A122148, A094289, A117579, A076265, A000040. Sequence in context: A212803 A002109 A259373 * A114876 A037980 A240626 Adjacent sequences:  A076262 A076263 A076264 * A076266 A076267 A076268 KEYWORD nonn,frac AUTHOR Jeff Burch, Nov 23 2002 EXTENSIONS Entry revised by N. J. A. Sloane, Apr 10 2006 Edited by N. J. A. Sloane, Aug 04 2008 at the suggestion of R. J. Mathar STATUS approved

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Last modified November 14 11:00 EST 2018. Contains 317182 sequences. (Running on oeis4.)