A317683 - OEIS

%I #15 Sep 21 2019 17:46:42

%S 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 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 6,6,7,6,9,4,4,5,9,5,9,5,4

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

%C As in A025441, the two squares must be distinct and positive.

%H Alois P. Heinz, <a href="/A317683/b317683.txt">Table of n, a(n) for n = 0..20000</a>

%F a(n) = Sum_{primes p} A025441(n-p).

%e a(12)=2 counts 12 = 7 +1^2 +2^2 = 2 + 1^2 +3^2.

%p A317683 := proc(n)

%p     a := 0 ;

%p     p := 2;

%p     while p <= n do

%p         a := a+A025441(n-p);

%p         p := nextprime(p) ;

%p     end do:

%p     a ;

%p end proc:

%t 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 Cf. A025441, A317682 - A317685.

%K nonn,easy

%O 0,13

%A _R. J. Mathar_, _Michel Marcus_, Aug 04 2018