A317684 Number of partitions of n into a prime and two squares.

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

Offset

0,4

Comments

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

Links

Table of n, a(n) for n=0..80.

C. Hooley, On the representation of a number as the sum of two squares and a prime, Acta Mathem. 97 (1957) 189-210

Formula

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

Example

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.

Maple

A317684 := proc(n)
    a := 0 ;
    p := 2;
    while p <= n do
        a := a+A000161(n-p);
        p := nextprime(p) ;
    end do:
    a ;
end proc:

Crossrefs

Cf. A000161, A317682-A317685.

Sequence in context: A304817 A242802 A277561 * A127973 A300654 A023157

Adjacent sequences: A317681 A317682 A317683 * A317685 A317686 A317687

Keyword

nonn,easy

Author

R. J. Mathar, Michel Marcus, Aug 04 2018

Status

approved