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Number of integer partitions of n containing no prime powers > 1.
11

%I #31 Dec 27 2020 03:35:14

%S 1,1,1,1,1,1,2,2,2,2,3,3,5,5,6,7,8,8,11,11,14,16,19,19,25,26,31,34,40,

%T 41,52,54,63,69,81,86,105,109,126,137,160,169,201,211,242,264,303,320,

%U 375,396,453,490,557,590,682,726,823,888,1002,1065,1219

%N Number of integer partitions of n containing no prime powers > 1.

%C First differs from A285798 at a(30) = 52, A285798(30) = 51.

%H Fausto A. C. Cariboni, <a href="/A321346/b321346.txt">Table of n, a(n) for n = 0..350</a>

%e The a(20) = 14 integer partitions:

%e (20)

%e (10,10)

%e (14,6)

%e (18,1,1)

%e (12,6,1,1)

%e (6,6,6,1,1)

%e (10,6,1,1,1,1)

%e (15,1,1,1,1,1)

%e (14,1,1,1,1,1,1)

%e (12,1,1,1,1,1,1,1,1)

%e (6,6,1,1,1,1,1,1,1,1)

%e (10,1,1,1,1,1,1,1,1,1,1)

%e (6,1,1,1,1,1,1,1,1,1,1,1,1,1,1)

%e (1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1)

%t nn=100;

%t ser=Product[If[PrimePowerQ[n],1,1/(1-x^n)],{n,nn}];

%t CoefficientList[Series[ser,{x,0,nn}],x]

%Y Cf. A000607, A000961, A001597, A002095, A023893, A023894, A096258, A246655, A320322, A321347, A321378, A321665, A322452, A322454.

%K nonn

%O 0,7

%A _Gus Wiseman_, Dec 11 2018