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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: A321738 A022458 A084419 * A034850 A220377 A145969

Adjacent sequences:  A119603 A119604 A119605 * A119607 A119608 A119609

KEYWORD

nonn

AUTHOR

Ryan Propper, Jun 04 2006

STATUS

approved

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Last modified December 12 11:56 EST 2018. Contains 318060 sequences. (Running on oeis4.)