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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 (list; graph; refs; listen; history; text; internal format)
 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: A255648 A112848 A229893 * A198727 A294508 A035152 Adjacent sequences:  A317680 A317681 A317682 * A317684 A317685 A317686 KEYWORD nonn,easy AUTHOR R. J. Mathar, Michel Marcus, Aug 04 2018 STATUS approved

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Last modified July 26 17:37 EDT 2021. Contains 346294 sequences. (Running on oeis4.)