A317684 - OEIS

%I #11 Aug 04 2018 11:15:29

%S 0,0,1,2,2,2,2,4,2,2,2,4,4,4,2,5,3,3,4,5,5,6,4,6,4,4,2,7,6,5,5,7,6,6,

%T 4,4,7,7,5,10,4,6,8,8,6,8,5,9,9,7,4,8,8,8,9,10,8,10,6,6,9,9,6,14,6,6,

%U 10,10,10,12,8,10,12,9,6,12,10,11,11,12,7

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

%C As in A000161, the squares may be zero and do not need to be distinct.

%H C. Hooley, <a href="https://projecteuclid.org/euclid.acta/1485892233">On the representation of a number as the sum of two squares and a prime</a>, Acta Mathem. 97 (1957) 189-210

%F a(n) = Sum_{primes p} A000161(n-p).

%e a(11) = 4 counts 11 = 11+0^2+0^2 = 7+0^2+2^2 = 2+0^2+3^2 = 3+2^2+2^2.

%p A317684 := proc(n)

%p     a := 0 ;

%p     p := 2;

%p     while p <= n do

%p         a := a+A000161(n-p);

%p         p := nextprime(p) ;

%p     end do:

%p     a ;

%p end proc:

%Y Cf. A000161, A317682-A317685.

%K nonn,easy

%O 0,4

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