A087942 Number of partitions of n into as many primes as n has prime factors.

0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 3, 1, 2, 1, 2, 1, 3, 1, 7, 1, 3, 7, 3, 1, 2, 1, 11, 1, 4, 0, 15, 1, 2, 1, 21, 1, 3, 1, 4, 12, 4, 1, 26, 1, 5, 0, 4, 1, 33, 1, 38, 0, 4, 1, 41, 1, 3, 19, 137, 0, 5, 1, 6, 1, 2, 1, 61, 1, 5, 22, 5, 0, 5, 1, 67, 24, 5, 1, 81, 1, 5, 0, 96, 1, 93, 1, 9, 0

Offset

1,10

Comments

Conjecture, for m>1: a(m)=0 iff n is an odd semiprime such that m-2 is not prime, i.e. m=A089268(k) for some k. - Reinhard Zumkeller, Oct 28 2003

Links

Table of n, a(n) for n=1..93.

Eric Weisstein's World of Mathematics, Prime Partition.

Index entries for sequences related to Goldbach conjecture

Example

n=20 = 2*2*5 = 13+5+2 = 11+7+2, all other partitions into 3 primes have fewer than or more than 3 parts, therefore a(20)=2.

Mathematica

Table[Count[IntegerPartitions[n, {PrimeOmega[n]}], _?(AllTrue[#, PrimeQ]&)], {n, 100}] (* Harvey P. Dale, Jul 26 2023 *)

Crossrefs

Cf. A001222, A000607, A051034, A004526.

Sequence in context: A363228 A235726 A060938 * A359237 A327925 A320012

Adjacent sequences: A087939 A087940 A087941 * A087943 A087944 A087945

Keyword

nonn

Author

Reinhard Zumkeller, Oct 27 2003

Status

approved