OFFSET
1,1
COMMENTS
Corresponding indices are listed in A141779(n) = {58, 282, 367, 743, 808, 1015, 1141, 1299, 1962, 2109, 2179, 2397, 2501, ...}.
Note that all listed terms are semiprime, for example: a(1) = 3599 = 59*61, a(2) = 118477 = 257*461, a(3) = 210589 = 251*839, a(4) = 971573 = 643*1511.
Conjecture: All terms are semiprime.
MATHEMATICA
Do[f=Numerator[Abs[(1 - Sum[Prime[k] + 1, {k, 1, n}])/Product[Prime[k] + 1, {k, 1, n}] ]]; If[ !PrimeQ[f]&&!(f==1), Print[{n, f, FactorInteger[f]}]], {n, 1, 8212}]
PROG
(PARI) for(n=1, 100, t=abs(numerator(matdet(matrix(n, n, i, j, if(i==j, prime(i)/(1+prime(i)), 1))))); if(t>3 && !isprime(t), print1(t", "))) \\ Charles R Greathouse IV, Feb 07 2013
CROSSREFS
Cf. A120292 = Absolute value of numerator of determinant of n X n matrix with elements M[i, j] = Prime[i]/(1+Prime[i]) if i=j and 1 otherwise. Cf. A125716 = Numbers n such that A120292(n) = 1. Cf. A141780 = Numbers n such that A120292(n) is prime. Cf. A141779 = Numbers n such that A120292(n)>1 and is not prime.
KEYWORD
nonn
AUTHOR
Alexander Adamchuk, Jul 04 2008
STATUS
approved