OFFSET
1,1
COMMENTS
Some a(n) are equal to 1 (n = 2, 3, 5, 7, 8, 9, 14, 15, 16, 17, 23, 31, 34, 35, 39, 41, 43, 50, 51, 56, ...).
a(58) = 3599 = 59*61 is not prime. - T. D. Noe, Nov 15 2006
Most terms are prime or 1.
Numbers n such that a(n)>1 and is not prime are listed in A141779(n) = {58, 282, 367, 743, 808, 1015, 1141, 1299, 1962, 2109, 2179, 2397, 2501, ...}.
Composite terms are listed in A141781 = {3599, 118477, 210589, 971573, 1164103, 1901959, 2446681, 3230069, ...}.
Note that all listed terms of A141781 are semiprime, for example: 3599 = 59*61, 118477 = 257*461, 210589 = 251*839, 971573 = 643*1511.
Conjecture: All composite terms are semiprime.
LINKS
Alexander Adamchuk, Jul 04 2008, Table of n, a(n) for n = 1..282
MATHEMATICA
Abs[Numerator[Table[Det[DiagonalMatrix[Table[Prime[i]/(Prime[i]+1)-1, {i, 1, n}]]+1], {n, 1, 60}]]]
Table[Numerator[Abs[(1 - Sum[Prime[k] + 1, {k, 1, n}])/Product[Prime[k] + 1, {k, 1, n}] ]], {n, 1, 282}]
PROG
(PARI) a(n)=abs(numerator(matdet(matrix(n, n, i, j, if(i==j, prime(i)/(1+prime(i)), 1))))) \\ Charles R Greathouse IV, Feb 07 2013
CROSSREFS
KEYWORD
frac,nonn
AUTHOR
Alexander Adamchuk, Jul 08 2006, Jul 04 2008
STATUS
approved