|
|
A072931
|
|
Number of ways to write n as a sum of 2 semiprimes.
|
|
10
|
|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,19
|
|
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
|
|
|
FORMULA
|
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
|
|
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++];
|
|
PROG
|
(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
|
|
CROSSREFS
|
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|