A035359 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

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

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

EXAMPLE

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)

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 *)

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.

KEYWORD

nonn,nice,hard,more

AUTHOR

EXTENSIONS

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

STATUS

approved