A091114 Number of partitions of n-th composite number containing the smallest prime factor: a(n) = A027293(A002808(n), A056608(n)).

2, 5, 11, 11, 22, 42, 77, 77, 135, 231, 385, 385, 627, 1002, 627, 1575, 1575, 2436, 3718, 5604, 5604, 8349, 5604, 12310, 17977, 17977, 26015, 37338, 53174, 53174, 75175, 105558, 53174, 147273, 147273, 204226, 281589, 204226, 386155, 386155

Offset: 1

Author

Reinhard Zumkeller, Feb 22 2004

Keywords

• nonn

Comments

a(n) = A000041(A002808(n)) - A091094(n).

a(n) = A000041(A085271(n)). - Charlie Neder, Jan 10 2019

Examples

			n=2: A002808(2)=6=2*3 has A000041(6)=11 partitions: 6 = 5+1 = 4+2 = 4+1+1 = 3+3 = 3+2+1 = 3+1+1+1 = 2+2+2 = 2+2+1+1 = 2+1+1+1+1 = 1+1+1+1+1+1, 2 occurs in 5 partitions, therefore a(2)=5.
		

Crossrefs

Cf. A002808, A000041, A020639, A027293, A056608, A085271, A091109, A091094.

Programs

PARI

lista(nn) = forcomposite(n=2, nn, print1(numbpart(n - divisors(n)[2]), ", ")); \\ Michel Marcus, Jan 11 2019