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A199331 Number of ordered ways of writing n as the sum of two semiprimes. 3
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 (list; graph; refs; listen; history; text; internal format)
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
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
Sequence in context: A007149 A028832 A260411 * A243917 A254212 A033773
KEYWORD
easy,nonn
AUTHOR
Robert G. Wilson v, Nov 05 2011
EXTENSIONS
Definition clarified by Robert Israel, Nov 24 2020
STATUS
approved

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Last modified March 28 05:39 EDT 2024. Contains 371235 sequences. (Running on oeis4.)