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A317683
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Number of partitions of n into a prime and two distinct positive squares.
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2
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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
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OFFSET
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0,13
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COMMENTS
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As in A025441, the two squares must be distinct and positive.
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LINKS
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FORMULA
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a(n) = Sum_{primes p} A025441(n-p).
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EXAMPLE
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a(12)=2 counts 12 = 7 +1^2 +2^2 = 2 + 1^2 +3^2.
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MAPLE
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a := 0 ;
p := 2;
while p <= n do
p := nextprime(p) ;
end do:
a ;
end proc:
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MATHEMATICA
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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 *)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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