A205601 Goldbach's problem extended to division: number of decompositions of 2n into the floor of unordered ratios of two primes, floor(q/p) = 2n, where p < 2n < q.

0, 1, 3, 5, 4, 5, 10, 5, 10, 16, 12, 17, 18, 16, 19, 27, 23, 22, 34, 27, 34, 39, 39, 45, 51, 41, 50, 51, 44, 57, 68, 71, 63, 74, 63, 76, 87, 84, 89, 104, 94, 108, 111, 99, 117, 116, 120, 104, 126, 114, 133, 146, 149, 146, 166, 148, 190, 178, 182, 170, 179, 173

Offset: 1

Author

James D. Klein, Jan 29 2012

Keywords

• nonn

Examples

			For n = 3, a(n) = 3 because 6 is the floor of 13/2, 19/3, and 31/5. - _T. D. Noe_, Jan 31 2012
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A002375, A202472.

Programs

Mathematica

Table[Length[Flatten[Table[Select[2*n*p + Range[p - 1], PrimeQ], {p, Prime[Range[PrimePi[2*n - 1]]]}]]], {n, 62}] (* T. D. Noe, Jan 31 2012 *)

PARI

a(n)=n*=2;my(s,t);forprime(p=2,n-1,t=n*p;while(n==(t=nextprime(t+1))\p,s++));s \\ Charles R Greathouse IV, Jan 30 2012

Extensions

a(21)-a(62) from Charles R Greathouse IV, Jan 31 2012