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%I #10 Feb 24 2019 01:56:59
%S 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,
%T 49,60,61,68,83,85,96,111,115,129,149,158,173,196,210,229,260,275,301,
%U 339,359,392,436,462,505,559,594,645,708,755,817,895,952,1026,1123,1194,1287
%N Number of partitions of n into primes or 1 where every part appears at least 3 times.
%H R. H. Hardin, <a href="/A161078/b161078.txt">Table of n, a(n) for n = 1..1000</a>
%F G.f.: -1+(1+x^3/(1-x))*product[1+x^{3*p(j)}/(1-x^{p(j)}, j=1..infinity], where p(j) is the j-th prime. - _Emeric Deutsch_, Jun 27 2009
%e a(12)=6 because we have 3333, 333111, 2^6, 22221111, 2221^6, and 1^(12). - _Emeric Deutsch_, Jun 27 2009
%p 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
%K nonn
%O 1,6
%A _R. H. Hardin_, Jun 02 2009
%E Definition edited to "primes or 1" by _R. H. Hardin_, Jun 22 2009
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