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Search: id:A141781
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| 3599, 118477, 210589, 971573, 1164103, 1901959, 2446681, 3230069, 2603767, 9114493, 9772927, 1497767, 6558967, 4323827, 32405449, 33992009, 11453957, 34417541, 35938783, 36569077, 40473001, 42110911, 47901839, 55183769
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OFFSET
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1,1
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COMMENT
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Corresponding numbers n such that A120292(n)>1 and is not prime are listed in A141779(n) = {58, 282, 367, 743, 808, 1015, 1141, 1299, 1962, 2109, 2179, 2397, 2501, ...}.
Note that all listed terms of a(n) 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 of a(n) are semiprime.
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FORMULA
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a(n) = A120292( A141779(n) ).
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MATHEMATICA
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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}]
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CROSSREFS
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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.
Adjacent sequences: A141778 A141779 A141780 this_sequence A141782 A141783 A141784
Sequence in context: A004932 A004952 A004972 this_sequence A096472 A027824 A068291
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KEYWORD
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nonn
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AUTHOR
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Alexander Adamchuk (alex(AT)kolmogorov.com), Jul 04 2008
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