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Composite terms of A120292: a(n) = A120292(A141779(n)).
3

%I #4 Feb 07 2013 22:57:48

%S 3599,118477,210589,971573,1164103,1901959,2446681,3230069,2603767,

%T 9114493,9772927,1497767,6558967,4323827,32405449,33992009,11453957,

%U 34417541,35938783,36569077,40473001,42110911,47901839,55183769

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

%C Corresponding indices are listed in A141779(n) = {58, 282, 367, 743, 808, 1015, 1141, 1299, 1962, 2109, 2179, 2397, 2501, ...}.

%C 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.

%C Conjecture: All terms are semiprime.

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

%t 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}]

%o (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

%Y 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.

%K nonn

%O 1,1

%A _Alexander Adamchuk_, Jul 04 2008