

A133850


Number of partitions of n into two primes and a semiprime.


1



0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 2, 3, 5, 3, 5, 3, 6, 7, 8, 4, 8, 6, 10, 8, 10, 7, 14, 10, 16, 12, 14, 9, 16, 14, 17, 12, 17, 16, 25, 15, 20, 20, 23, 20, 25, 20, 28, 22, 25, 23, 30, 23, 31, 28, 33, 28, 35, 32, 36, 30, 33, 32, 44, 35, 34, 37, 42, 43, 49, 39, 42, 42, 44, 49, 49, 40, 45, 51
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OFFSET

1,10


COMMENTS

This was inspired by the fact that our universe seems to be 73% Dark Energy, 23% Dark Matter and 4% ordinary matter, where 73 is prime, 23 is prime, 4 is semiprime.


REFERENCES

Guy Gugliotta, "Mining for Dark Matter", Discover, May 2007, 3641. "Dark energy makes up 73 percent of the universe, dark matter another 23 percent. Atomic matter  everything around us and everything astronomers have ever seen  accounts for just 4 percent."


LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..5000


EXAMPLE

Examples:
n a(n)
07 0
8 1 2+2+4,
9 1 2+3+4,
10 2 2+2+6 = 3+3+4,
11 2 2+3+6 = 2+5+4,
12 2 3+3+6 = 3+5+4,
13 3 2+2+9 = 2+5+6 = 2+7+4,
14 5 2+2+10 = 2+3+9 = 3+5+6 = 3+7+4 = 5+5+4,
15 3 2+3+10 = 2+7+6 = 3+3+9,
16 5 2+5+9 = 3+3+10 = 3+7+6 = 5+5+6 = 5+7+4,
17 3 2+5+10 = 2+11+4 = 3+5+9,
18 6 2+2+14 = 2+7+9 = 3+5+10 = 3+11+4 = 5+7+6 = 7+7+4, etc.


MATHEMATICA

semiPrimeQ[x_] := Plus @@ Last /@ FactorInteger[x] == 2; f[n_] := Block[{c = 0, i = j = 1, p = PrimePi[(n  4)/2]}, While[i < p + 1, j = i; q = PrimePi[n  4  Prime@i]; While[j < q + 1, If[semiPrimeQ[n  Prime@i  Prime@j], c++ ]; j++ ]; i++ ]; c]; Array[f, 70] (* Robert G. Wilson v *)


CROSSREFS

Cf. A000040, A001358, A000002.
Sequence in context: A228405 A276824 A235998 * A160902 A082408 A270566
Adjacent sequences: A133847 A133848 A133849 * A133851 A133852 A133853


KEYWORD

nonn


AUTHOR

Jonathan Vos Post, Jan 21 2008


EXTENSIONS

More terms from Robert G. Wilson v, Jan 21 2008


STATUS

approved



