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)/(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
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
KEYWORD
nonn,frac,easy
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