A141779 Numbers k such that A120292(k) is composite.

58, 282, 367, 743, 808, 1015, 1141, 1299, 1962, 2109, 2179, 2397, 2501, 3704, 3825, 3912, 3932, 3935, 4016, 4049, 4247, 4327, 4598, 4915, 4977, 5210, 5266, 5396, 5420, 5512, 5562, 5773, 5981, 6031, 6249, 6616, 6984, 7117, 7121, 7304, 7338, 7424, 7653

Offset

1,1

Comments

Composite terms of A120292 are listed in A141781 = {3599, 118477, 210589, 971573, 1164103, 1901959, 2446681, 3230069, ...}.

Note that all listed terms correspond to semiprimes, for example: 3599 = 59*61, 118477 = 257*461, 210589 = 251*839, 971573 = 643*1511.

Conjecture: All composite terms of A120292 are semiprime.

Links

Table of n, a(n) for n=1..43.

Formula

A141781(n) = A120292( a(n) ).

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(n", "))) \\ 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 (k such that A120292(k) = 1).

Cf. A141780 (k such that A120292(k) is prime).

Cf. A141781 (terms of A120292 that are greater than 1 and are not prime; or A120292(A141779)).

Sequence in context: A334186 A051972 A027987 * A250927 A250920 A235673

Adjacent sequences: A141776 A141777 A141778 * A141780 A141781 A141782

Keyword

nonn

Author

Alexander Adamchuk, Jul 04 2008

Status

approved