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%I #11 Jun 07 2021 04:42:46
%S 58,282,367,743,808,1015,1141,1299,1962,2109,2179,2397,2501,3704,3825,
%T 3912,3932,3935,4016,4049,4247,4327,4598,4915,4977,5210,5266,5396,
%U 5420,5512,5562,5773,5981,6031,6249,6616,6984,7117,7121,7304,7338,7424,7653
%N Numbers k such that A120292(k) is composite.
%C Composite terms of A120292 are listed in A141781 = {3599, 118477, 210589, 971573, 1164103, 1901959, 2446681, 3230069, ...}.
%C Note that all listed terms correspond to semiprimes, for example: 3599 = 59*61, 118477 = 257*461, 210589 = 251*839, 971573 = 643*1511.
%C Conjecture: All composite terms of A120292 are semiprime.
%F A141781(n) = A120292( a(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(n", "))) \\ _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.
%Y Cf. A125716 (k such that A120292(k) = 1).
%Y Cf. A141780 (k such that A120292(k) is prime).
%Y Cf. A141781 (terms of A120292 that are greater than 1 and are not prime; or A120292(A141779)).
%K nonn
%O 1,1
%A _Alexander Adamchuk_, Jul 04 2008
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