OFFSET
1,2
COMMENTS
Many a(n) are equal to 1. The indices n such that a(n) = 1 are listed in A051838[n] = {1,3,8,13,23,38,39,41,43,48,50,53,56,57,58,66,68,70,73,77,84,90,94,98,...}. Primes p such that a(p) = 1 are listed in A121756[n] = {3,13,23,41,43,53,73,149,151,157,167,191,229,269,293,373,521,557,569,607,691, 701,829,853,863,887,947,991,...}. Many a(n) are primes. It appears that all prime a(n) {5,17,2,41,29,43,197,281,127,167,3,113,457,617,709,809,1277,1409,317,2027,307,...} and all prime divisors of composite a(n) {2,5,71,89,3,107,569,7,383,331,457,...} belong to A111267[n].
LINKS
Harvey P. Dale, Table of n, a(n) for n = 1..10000
FORMULA
MATHEMATICA
Table[Numerator[Sum[Prime[k], {k, 1, n}]/Product[Prime[k], {k, 1, n}]], {n, 1, 100}]
Module[{prs=Prime[Range[70]]}, Flatten[Numerator[Thread[ {Accumulate[ prs]/ Rest[ FoldList[Times, 1, prs]]}]]]] (* This is several hundred times faster than the first Mathematica program in generating 5000 terms of the sequence *) (* Harvey P. Dale, Dec 29 2012 *)
CROSSREFS
KEYWORD
frac,nonn
AUTHOR
Alexander Adamchuk, Aug 19 2006
STATUS
approved