

A119606


Number of primes of the form f(n) + 1, where f(n) is the product of one or more divisors of n.


0



1, 2, 1, 3, 1, 6, 1, 4, 1, 4, 1, 11, 1, 4, 1, 5, 1, 10, 1, 9, 1, 3, 1, 19, 1, 4, 1, 7, 1, 26, 1, 5, 1, 2, 1, 25, 1, 2, 1, 14, 1, 25, 1, 6, 1, 3, 1, 30, 1, 6, 1, 6, 1, 16, 1, 12, 1, 3, 1, 81, 1, 2, 1, 6, 1, 18, 1, 5, 1, 18, 1, 41, 1, 4, 1, 3, 1, 22, 1, 20, 1, 3, 1, 71, 1, 3, 1, 11, 1, 76, 1, 5, 1, 3, 1, 38
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,2


LINKS

Table of n, a(n) for n=1..96.


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 adding 1 yields {1, 2, 3, 5, 3, 5, 9, 9}, of which the primes are {2, 3, 5}.


MATHEMATICA

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


CROSSREFS

Sequence in context: A152063 A022458 A084419 * A034850 A220377 A145969
Adjacent sequences: A119603 A119604 A119605 * A119607 A119608 A119609


KEYWORD

nonn


AUTHOR

Ryan Propper, Jun 04 2006


STATUS

approved



