A280830 Number of partitions of n into two products-of-three-primes.

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, 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, 1, 3, 2, 4, 1, 2, 2, 1, 1, 3, 1, 3, 1, 2, 2, 3, 0, 4, 2, 4, 1, 4

Offset

1,36

Links

Indranil Ghosh, Table of n, a(n) for n = 1..1000

Index entries for sequences related to partitions

Formula

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

Example

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

Maple

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);

Mathematica

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 *)

Prog

(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

Crossrefs

Cf. A014612, A101605.

Sequence in context: A294658 A127543 A353237 * A068907 A219762 A227696

Adjacent sequences: A280827 A280828 A280829 * A280831 A280832 A280833

Keyword

nonn,easy

Author

Wesley Ivan Hurt, Jan 08 2017

Status

approved