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A141779 Numbers n such that A120292(n) is composite. 4
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 (list; graph; refs; listen; history; text; internal format)
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 = Numbers n such that A120292(n) = 1. Cf. A141780 = Numbers n such that A120292(n) is prime. Cf. A141781 = Terms of A120292(n) that are greater than 1 and are not prime; or A120292( A141779(n) ).

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

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Last modified May 10 23:31 EDT 2021. Contains 343784 sequences. (Running on oeis4.)