A298604 - OEIS

%I #4 Jan 22 2018 18:42:44

%S 1,1,0,1,1,1,1,1,2,1,1,2,2,2,2,2,3,3,3,4,4,4,4,5,6,5,5,6,6,7,7,8,9,8,

%T 9,10,11,12,11,12,14,14,15,16,17,17,17,20,22,21,22,24,25,27,28,30,31,

%U 31,33,36,39,40,40,42,46,47,49,53,54,55,58,63,67,68,70,73,77,81,84

%N Number of partitions of n into distinct odd prime parts (including 1).

%H <a href="/index/Par#part">Index entries for related partition-counting sequences</a>

%F G.f.: (1 + x)*Product_{k>=2} (1 + x^prime(k)).

%e a(16) = 3 because we have [13, 3], [11, 5] and [7, 5, 3, 1].

%t nmax = 78; CoefficientList[Series[(1 + x) Product[(1 + x^Prime[k]), {k, 2, nmax}], {x, 0, nmax}], x]

%Y Cf. A000586, A006005, A008578, A024939, A036497, A298603.

%K nonn

%O 0,9

%A _Ilya Gutkovskiy_, Jan 22 2018