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

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

Offset: 1

Author

Jeff Burch, Nov 23 2002

Keywords

• nonn
• frac
• easy

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)/(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

Examples

			A122148(n)/a(n) begins 1/4, 23/108, 71983/337500, ... - _Alexander Adamchuk_, Aug 22 2006
		

Crossrefs

Cf. A051674, A122147, A122148, A094289, A117579, A076265, A000040.

Programs

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 *)

PARI

a(n)=prod(i=1,n,prime(i)^prime(i)) \\ Charles R Greathouse IV, Aug 05 2015

Formula

log a(n) ~ (n^2 log^2 n)/2. - Charles R Greathouse IV, Sep 14 2015

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