A084419 a(n) = number of primes that can be formed by adding 1 to the product of any subset of the divisors of n.

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

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: A321738 A022458 A377510 * 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