A035359 Number of partitions-into-distinct-parts of n (A000009) is a prime.

3, 4, 5, 7, 22, 70, 100, 495, 1247, 2072, 320397, 3335367, 16168775, 37472505, 52940251, 78840125, 81191852

Offset: 1

Author

Olivier Gérard

Keywords

• nonn
• nice
• hard
• more

Comments

No other terms below 10^8. - Max Alekseyev, Jul 10 2015

Examples

			From _Gus Wiseman_, Jan 13 2020: (Start)
Strict partitions of a(1) = 3 through a(4) = 7:
  (3)    (4)    (5)    (7)
  (2,1)  (3,1)  (3,2)  (4,3)
                (4,1)  (5,2)
                       (6,1)
                       (4,2,1)
(End)
		

Links

• Eric Weisstein's World of Mathematics, Integer Sequence Primes
• Eric Weisstein's World of Mathematics, Partition Function Q
• Eric Weisstein's World of Mathematics, Partition Function Q-Congruences

Crossrefs

The non-strict version is A046063.

The version for powers of 2 instead of primes is A331022.

The version for factorizations instead of strict partitions is A330991.

The version for strict factorizations instead of strict partitions is A331201.

Cf. A000009, A051005, A056848, A265835.

Programs

Mathematica

n = 1; A035359 = {}; While[n < 10^7, n++; If[ PrimeQ[ PartitionsQ[n]], Print[n]; AppendTo[A035359, n]]]; A035359 (* Jean-François Alcover, Oct 12 2011 *)

Extensions

More terms from Eric W. Weisstein

a(12) from Max Alekseyev, Jul 04 2009

a(13)-a(14) from Giovanni Resta, Jun 05 2015, Jun 11 2015

a(15)-a(17) from Max Alekseyev, Jul 10 2015