A199331 Number of ordered ways of writing n as the sum of two semiprimes.

0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 1, 2, 2, 2, 2, 0, 3, 4, 3, 2, 0, 2, 4, 4, 2, 2, 3, 4, 5, 6, 4, 0, 2, 6, 6, 4, 2, 6, 6, 4, 5, 8, 7, 4, 2, 8, 10, 6, 5, 2, 5, 6, 4, 10, 6, 4, 4, 10, 12, 12, 2, 6, 10, 6, 7, 8, 9, 6, 5, 12, 14, 10, 6, 6, 7, 8, 7, 10, 10, 6, 4, 14, 14

Offset

1,10

Comments

Conjecture: Only the integers 1, 2, 3, 4, 5, 6, 7, 9, 11, 17, 22, 33 (A072966) cannot be partitioned into a set of two semiprimes.

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Formula

a(n) = Sum_{k=1..n-1} c(k) * c(n-k), where c = A064911. - Wesley Ivan Hurt, Jan 07 2024

Maple

sp:= select(t -> numtheory:-bigomega(t)=2, [$1..100]):
G:= expand(add(x^t, t=sp)^2):
seq(coeff(G, x, i), i=1..100); # Robert Israel, Nov 24 2020

Mathematica

mx=200; semiPrimeQ[n_] := Plus @@ Last /@ FactorInteger@ n == 2; t = Select[ Range@ mx, semiPrimeQ]; s = Sort[Plus @@@ Tuples[t, 2]]; Transpose[ Tally@ Join[ Range@ mx, s]][[2]] - 1

Crossrefs

Cf. A001358, A035026, A064911, A072966, A073610.

Sequence in context: A007149 A028832 A260411 * A243917 A254212 A033773

Adjacent sequences: A199328 A199329 A199330 * A199332 A199333 A199334

Keyword

easy,nonn

Author

Robert G. Wilson v, Nov 05 2011

Extensions

Definition clarified by Robert Israel, Nov 24 2020

Status

approved