

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
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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: A181481 A239489 A259759 * A279968 A164297 A109578
Adjacent sequences: A119604 A119605 A119606 * A119608 A119609 A119610


KEYWORD

nonn


AUTHOR

Ryan Propper, Jun 04 2006


STATUS

approved



