A280829 Number of partitions of n into two squarefree semiprimes.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 2, 1, 0, 0, 1, 1, 0, 1, 2, 1, 1, 1, 2, 0, 0, 1, 3, 1, 0, 1, 2, 2, 1, 2, 3, 2, 0, 2, 4, 3, 1, 0, 3, 2, 2, 2, 3, 2, 0, 2, 4, 5, 0, 1, 2, 3, 2, 3, 5, 2, 2, 3, 7, 4, 1, 2, 3, 4, 2, 5, 4, 2, 0, 4, 6, 2, 2, 2, 4, 3, 4

Offset

1,20

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)} A280710(i) * A280710(n-i).

Example

a(20) = 2; there are 2 partitions of 20 into two squarefree semiprimes: (14,6) and (10,10).

Maple

with(numtheory): A280829:=n->add(floor(bigomega(i)*mobius(i)^2/2)*floor(2*mobius(i)^2/bigomega(i))*floor(bigomega(n-i)*mobius(i)^2/2)*floor(2*mobius(n-i)^2/bigomega(n-i)), i=2..floor(n/2)): seq(A280829(n), n=1..100);

Mathematica

Table[Sum[Floor[PrimeOmega[i] MoebiusMu[i]^2 / 2] Floor[2 MoebiusMu[i]^2 / PrimeOmega[i]] Floor[PrimeOmega[n - i] MoebiusMu[i]^2 / 2] Floor[2 MoebiusMu[n - i]^2 / PrimeOmega[n - i]], {i, 2, Floor[n/2]}], {n, 1, 90}] (* Indranil Ghosh, Mar 10 2017, translated from Maple code *)

Prog

(PARI) for(n=1, 90, print1(sum(i=2, floor(n/2), floor(bigomega(i) * moebius(i)^2 / 2) * floor(2 * moebius(i)^2 / bigomega(i)) * floor(bigomega(n - i) * moebius(i)^2 / 2) * floor(2 * moebius(n - i)^2 / bigomega(n - i))), ", ")) \\ Indranil Ghosh, Mar 10 2017

Crossrefs

Cf. A006881, A071068, A280710.

Sequence in context: A056929 A304096 A151692 * A303942 A321928 A321917

Adjacent sequences: A280826 A280827 A280828 * A280830 A280831 A280832

Keyword

nonn,easy

Author

Wesley Ivan Hurt, Jan 08 2017

Status

approved