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A317683
Number of partitions of n into a prime and two distinct positive squares.
2
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
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
KEYWORD
nonn,easy
AUTHOR
STATUS
approved