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Number of partitions of n into two products-of-three-primes.
1

%I #15 Jan 29 2018 06:29:44

%S 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0,

%T 1,2,0,2,1,2,0,1,0,0,1,1,1,2,0,2,0,1,1,2,1,2,2,2,0,3,0,3,1,2,1,0,0,1,

%U 1,3,2,4,1,2,2,1,1,3,1,3,1,2,2,3,0,4,2,4,1,4

%N Number of partitions of n into two products-of-three-primes.

%H Indranil Ghosh, <a href="/A280830/b280830.txt">Table of n, a(n) for n = 1..1000</a>

%H <a href="/index/Par#part">Index entries for sequences related to partitions</a>

%F a(n) = Sum_{i=2..floor(n/2)} A101605(i) * A101605(n-i).

%e a(36) = 2; there are 2 partitions of 36 into two products-of-three-primes: (28,8) and (18,18).

%p with(numtheory): A280830:=n->add(floor(bigomega(i)/3)*floor(3/bigomega(i))*floor(3/bigomega(n-i))*floor(bigomega(n-i)/3), i=2..floor(n/2)): seq(A280830(n), n=1..100);

%t Table[Sum[Floor[PrimeOmega[i]/3] Floor[3/PrimeOmega[i]] Floor[3/PrimeOmega[n - i]] Floor[PrimeOmega[n - i]/3], {i, 2, Floor[n/2]}],{n, 1, 90}] (* _Indranil Ghosh_, Mar 09 2017, translated from Maple code *)

%o (PARI) for(n=1, 90, print1(sum(i=2, floor(n/2), floor(bigomega(i)/3) * floor(3/bigomega(i)) * floor(3/bigomega(n - i)) * floor(bigomega(n - i)/3)),", ")) \\ _Indranil Ghosh_, Mar 09 2017

%Y Cf. A014612, A101605.

%K nonn,easy

%O 1,36

%A _Wesley Ivan Hurt_, Jan 08 2017