A112528 Number of representations of n-th prime of the form p1*p2+p3, where p1, p2 and p3 are primes, not necessarily all distinct.

0, 0, 0, 1, 3, 2, 5, 2, 4, 4, 2, 5, 6, 4, 4, 6, 4, 3, 6, 5, 4, 6, 4, 8, 7, 6, 5, 6, 6, 9, 6, 7, 8, 5, 8, 6, 7, 10, 5, 9, 8, 6, 6, 7, 10, 7, 9, 9, 6, 9, 12, 11, 7, 8, 11, 8, 11, 8, 11, 12, 9, 11, 13, 9, 10, 14, 13, 13, 7, 9, 12, 12, 12, 14, 11, 11, 15, 13, 15, 12, 13, 9, 12, 12, 13, 14, 13, 14, 13

Offset: 1

Author

Zak Seidov, Sep 10 2005

Keywords

• nonn

Comments

a(n) = Sum(A064911(A000040(n)-A000040(k)): 1<=kReinhard Zumkeller, Sep 22 2005

Examples

			No solutions for 2,3,5;
7=2*2+3, 11=2*2+7=2*3+5=3*3+2, 13=2*3+7=2*5+3, 17=2*2+13=2*3+11=2*5+7=2*7+3=3*5+2,
19=2*3+13, 23=2*2+19=2*3+17=2*5+13=3*7+2, 29=2*3+23=2*5+19=2*11+7=2*13+3,
31=2*7+17=2*13+5, ...
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..1000

Programs

Mathematica

Table[Function[q, Length@ DeleteCases[#, s_ /; Length@s != 3] &@ Map[Flatten[ FactorInteger[#] /. {{p_, e_} /; p > 1 :> ConstantArray[p, e], {1, 1} -> 1}] &, Select[IntegerPartitions[q, {2}], And[! MemberQ[#, 1], Total@ Boole@ PrimeQ@ # == 1] &]]]@ Prime@ n, {n, 89}] (* Michael De Vlieger, May 01 2017 *)

Extensions

More terms from Reinhard Zumkeller, Sep 22 2005