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

Author

Reinhard Zumkeller, Oct 27 2003

Keywords

• nonn

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

Examples

			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.
		

Links

• Eric Weisstein's World of Mathematics, Prime Partition.
• Index entries for sequences related to Goldbach conjecture

Crossrefs

Cf. A001222, A000607, A051034, A004526.

Programs

Mathematica

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