cp's OEIS Frontend

A317683 Number of partitions of n into a prime and two distinct positive squares.

%I A317683 #15 Sep 21 2019 17:46:42
%S A317683 0,0,0,0,0,0,0,1,1,0,1,0,2,1,0,2,2,1,2,1,2,1,3,2,3,1,1,3,4,2,3,3,3,3,
%T A317683 3,0,6,3,1,5,3,2,6,4,4,3,4,4,7,2,3,4,5,4,6,4,5,7,6,2,7,3,2,9,6,3,7,5,
%U A317683 6,6,7,6,9,4,4,5,9,5,9,5,4
%N A317683 Number of partitions of n into a prime and two distinct positive squares.
%C A317683 As in A025441, the two squares must be distinct and positive.
%H A317683 Alois P. Heinz, <a href="/A317683/b317683.txt">Table of n, a(n) for n = 0..20000</a>
%F A317683 a(n) = Sum_{primes p} A025441(n-p).
%e A317683 a(12)=2 counts 12 = 7 +1^2 +2^2 = 2 + 1^2 +3^2.
%p A317683 A317683 := proc(n)
%p A317683     a := 0 ;
%p A317683     p := 2;
%p A317683     while p <= n do
%p A317683         a := a+A025441(n-p);
%p A317683         p := nextprime(p) ;
%p A317683     end do:
%p A317683     a ;
%p A317683 end proc:
%t A317683 p2sQ[n_]:=Length[Union[n]]==3&&Count[n,_?(IntegerQ[Sqrt[#]]&)]==2&&Count[ n,_?(PrimeQ[#]&)]==1; Table[Count[IntegerPartitions[n,{3}],_?p2sQ],{n,0,80}] (* _Harvey P. Dale_, Sep 21 2019 *)
%Y A317683 Cf. A025441, A317682 - A317685.
%K A317683 nonn,easy
%O A317683 0,13
%A A317683 _R. J. Mathar_, _Michel Marcus_, Aug 04 2018