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

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, 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, 6, 6, 7, 6, 9, 4, 4, 5, 9, 5, 9, 5, 4

Offset

0,13

Comments

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

Links

Alois P. Heinz, Table of n, a(n) for n = 0..20000

Formula

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

Example

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

Maple

A317683 := proc(n)
    a := 0 ;
    p := 2;
    while p <= n do
        a := a+A025441(n-p);
        p := nextprime(p) ;
    end do:
    a ;
end proc:

Mathematica

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 *)

Crossrefs

Cf. A025441, A317682 - A317685.

Sequence in context: A112848 A374366 A229893 * A366371 A198727 A294508

Adjacent sequences: A317680 A317681 A317682 * A317684 A317685 A317686

Keyword

nonn,easy

Author

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

Status

approved