A141781 Composite terms of A120292: a(n) = A120292(A141779(n)).

3599, 118477, 210589, 971573, 1164103, 1901959, 2446681, 3230069, 2603767, 9114493, 9772927, 1497767, 6558967, 4323827, 32405449, 33992009, 11453957, 34417541, 35938783, 36569077, 40473001, 42110911, 47901839, 55183769

Offset: 1

Author

Alexander Adamchuk, Jul 04 2008

Keywords

• nonn

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.

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.

Programs

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}]

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

Formula

a(n) = A120292(A141779(n)).