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A084419 a(n) = number of primes that can be formed by adding 1 to the product of any subset of the divisors of n. 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

a(2n-1) = 1.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..1000

EXAMPLE

a(6) = 6: the divisors of 6 are 1, 2, 3 and 6 and the divisor products are 1, 2, 3, 6, 12, 18 and 36; the primes arising are 2, 3, 7, 13, 19 and 37.

a(12) = 11 = #{2, 3, 5, 7, 13, 19, 37, 73, 97, 433, 577}.

MATHEMATICA

Table[Count[Union[Times@@@Subsets[Divisors[n], DivisorSigma[0, n]]]+1, _?PrimeQ], {n, 100}] (* Harvey P. Dale, Jun 24 2013 *)

CROSSREFS

Cf. A119607.

Sequence in context: A347982 A321738 A022458 * A119606 A034850 A220377

Adjacent sequences:  A084416 A084417 A084418 * A084420 A084421 A084422

KEYWORD

nonn

AUTHOR

Amarnath Murthy, Jun 01 2003

EXTENSIONS

More terms from David Wasserman, Dec 28 2004

Corrected by Harvey P. Dale, Jun 24 2013

STATUS

approved

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Last modified January 18 10:47 EST 2022. Contains 350454 sequences. (Running on oeis4.)