login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

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