A072931 Number of ways to write n as a sum of 2 semiprimes.

0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 2, 2, 2, 1, 0, 1, 2, 2, 1, 1, 2, 2, 3, 3, 2, 0, 1, 3, 3, 2, 1, 3, 3, 2, 3, 4, 4, 2, 1, 4, 5, 3, 3, 1, 3, 3, 2, 5, 3, 2, 2, 5, 6, 6, 1, 3, 5, 3, 4, 4, 5, 3, 3, 6, 7, 5, 3, 3, 4, 4, 4, 5, 5, 3, 2, 7, 7, 2, 4, 4, 5, 4, 6, 8, 6, 3, 3, 8, 7, 7, 4, 6, 8, 6, 5, 7, 7, 2

Offset: 0

Author

Benoit Cloitre, Aug 13 2002

Keywords

• easy
• look
• nonn

Comments

Sequence is probably > 0 for n > 33.

The graph of this sequence is compelling evidence that 33 is the last term of sequence A072966. - T. D. Noe, Apr 10 2007

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..20000 (first 10000 terms from T. D. Noe)

Crossrefs

Cf. A001222, A001358, A072966, A101048.

Column k=2 of A344447.

Programs

Mathematica

lim = 10000;
s = Select[Range[lim], PrimeOmega[#] == 2 &];
c = Tally[ Sort[ Map[ Total, Union[Subsets[s, {2}],
      Table[{s[[i]], s[[i]]}, {i, 1, Length[s]}]]]]];
a = Table[0, lim];
i=1; While[c[[i]] [[1]]<=lim, a[[c[[i]] [[1]]]]=c[[i]] [[2]]; i++];
a (* Robert Price, Mar 30 2019 *)

PARI

a(n)=sum(i=1, n, sum(j=1, i, if(abs(bigomega(i)-2) + abs(bigomega(j)-2) + abs(n-i-j),0,1)))

PARI

a(n)=my(s); forprime(p=2,n\4, forprime(q=2,min(n\(2*p),p), if(bigomega(n-p*q)==2, s++))); s \\ Charles R Greathouse IV, Dec 07 2014

Formula

From Reinhard Zumkeller, Jan 21 2010: (Start)

a(A100592(n)) = n;

a(m) < n for m < A100592(n);

A171963(n) = a(A001358(n)). (End)

a(n) = Sum_{i=1..floor(n/2)} [Omega(i) == 2] * [Omega(n-i) == 2], where Omega = A001222 and [] is the Iverson Bracket. - Wesley Ivan Hurt, Apr 04 2018

a(n) = [x^n y^2] 1/Product_{j>=1} (1-y*x^A001358(j)). - Alois P. Heinz, May 21 2021