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A119607 Number of primes of the form f(n) - 1, where f(n) is the product of one or more divisors of n. 2
0, 0, 1, 2, 0, 4, 0, 3, 1, 1, 0, 11, 0, 2, 1, 4, 0, 8, 0, 6, 1, 2, 0, 18, 0, 1, 1, 6, 0, 25, 0, 5, 1, 2, 0, 21, 0, 1, 1, 11, 0, 25, 0, 5, 1, 0, 0, 27, 0, 4, 1, 5, 0, 13, 0, 11, 1, 0, 0, 83, 0, 1, 1, 7, 0, 17, 0, 7, 1, 11, 0, 34, 0, 1, 1, 7, 0, 15, 0, 17, 1, 2, 0, 71, 0, 1, 1, 7, 0, 66, 0, 6, 1, 0, 0, 36 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..2000

EXAMPLE

The divisors of 4 are D = {1, 2, 4} and the subsets of D are {{}, {1}, {2}, {4}, {1, 2}, {1, 4}, {2, 4}, {1, 2, 4}}. Taking the product of elements in these subsets and subtracting 1 yields {-1, 0, 1, 3, 1, 3, 7, 7}, of which the primes are {3, 7}.

MATHEMATICA

Do[l = Subsets[Divisors[n]]; l = Union[Map[Times @@ # - 1&, l]]; Print[Length[Select[l, PrimeQ]]], {n, 100}]

CROSSREFS

Cf. A084419.

Sequence in context: A053118 A181481 A239489 * A164297 A109578 A082519

Adjacent sequences:  A119604 A119605 A119606 * A119608 A119609 A119610

KEYWORD

nonn

AUTHOR

Ryan Propper, Jun 04 2006

STATUS

approved

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Last modified November 26 16:10 EST 2014. Contains 250079 sequences.