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 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. 1
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 LINKS Charles R Greathouse IV, Table of n, a(n) for n = 1..10000 EXAMPLE 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 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 *) PROG (C++) #include using namespace std; int main() //C++ code for the first 20 even integers >= 2            //where floor(q/p) = 2n, p<2np[istart]) istart++;     count = 0;     for(int j=0; p[j]<2*n; j++)       for(int i=istart; p[i]<(p[j]+1)*2*n; i++)         if(p[i]/p[j]==2*n)count++;       cout << n << ". " << count << endl;   } return 0; } (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 CROSSREFS Cf. A002375, A202472. Sequence in context: A206035 A200100 A057759 * A021286 A200324 A063259 Adjacent sequences:  A205598 A205599 A205600 * A205602 A205603 A205604 KEYWORD nonn AUTHOR James D. Klein, Jan 29 2012 EXTENSIONS a(21)-a(62) from Charles R Greathouse IV, Jan 31 2012 STATUS approved

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Last modified April 18 05:11 EDT 2021. Contains 343072 sequences. (Running on oeis4.)