A161078 Number of partitions of n into primes or 1 where every part appears at least 3 times.

0, 0, 1, 1, 1, 2, 1, 2, 3, 3, 3, 6, 5, 6, 10, 8, 9, 14, 13, 16, 21, 19, 23, 30, 31, 34, 42, 44, 49, 60, 61, 68, 83, 85, 96, 111, 115, 129, 149, 158, 173, 196, 210, 229, 260, 275, 301, 339, 359, 392, 436, 462, 505, 559, 594, 645, 708, 755, 817, 895, 952, 1026, 1123, 1194, 1287

Offset: 1

Author

R. H. Hardin, Jun 02 2009

Keywords

• nonn

Examples

			a(12)=6 because we have 3333, 333111, 2^6, 22221111, 2221^6, and 1^(12). - _Emeric Deutsch_, Jun 27 2009
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A161077.

Programs

Maple

g := -1+(1+x^3/(1-x))*(product(1+x^(3*ithprime(j))/(1-x^ithprime(j)), j = 1 .. 20)): gser := series(g, x = 0, 75): seq(coeff(gser, x, n), n = 2 .. 65); # Emeric Deutsch, Jun 27 2009

Formula

G.f.: -1+(1+x^3/(1-x))*Product_{j>=1} ( 1+x^(3*p(j))/(1-x^(p(j))) ), where p(j) is the j-th prime. - Emeric Deutsch, Jun 27 2009

Extensions

Definition edited to "primes or 1" by R. H. Hardin, Jun 22 2009