A076265 a(n) = Product_{i=1..n} prime(i)^prime(i).

4, 108, 337500, 277945762500, 79301169838123235887500, 24018350267611933650627567399079537500, 19868946365457062696924774946056904675112420776003728137500

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

Table of n, a(n) for n=1..7.

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