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%I #13 Jul 26 2023 13:33:49
%S 0,1,1,1,1,1,1,1,1,2,1,2,1,2,1,3,1,2,1,2,1,3,1,7,1,3,7,3,1,2,1,11,1,4,
%T 0,15,1,2,1,21,1,3,1,4,12,4,1,26,1,5,0,4,1,33,1,38,0,4,1,41,1,3,19,
%U 137,0,5,1,6,1,2,1,61,1,5,22,5,0,5,1,67,24,5,1,81,1,5,0,96,1,93,1,9,0
%N Number of partitions of n into as many primes as n has prime factors.
%C Conjecture, for m>1: a(m)=0 iff n is an odd semiprime such that m-2 is not prime, i.e. m=A089268(k) for some k. - _Reinhard Zumkeller_, Oct 28 2003
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PrimePartition.html">Prime Partition.</a>
%H <a href="/index/Go#Goldbach">Index entries for sequences related to Goldbach conjecture</a>
%e n=20 = 2*2*5 = 13+5+2 = 11+7+2, all other partitions into 3 primes have fewer than or more than 3 parts, therefore a(20)=2.
%t Table[Count[IntegerPartitions[n,{PrimeOmega[n]}],_?(AllTrue[#,PrimeQ]&)],{n,100}] (* _Harvey P. Dale_, Jul 26 2023 *)
%Y Cf. A001222, A000607, A051034, A004526.
%K nonn
%O 1,10
%A _Reinhard Zumkeller_, Oct 27 2003
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