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A117119 Number of partitions of 2*n into two odd prime powers. 1
1, 1, 2, 2, 3, 3, 4, 3, 4, 4, 4, 4, 5, 5, 6, 6, 6, 6, 6, 5, 6, 6, 6, 7, 8, 6, 9, 7, 6, 8, 7, 6, 8, 7, 7, 9, 8, 7, 9, 8, 7, 11, 9, 7, 12, 8, 7, 9, 9, 8, 10, 8, 9, 12, 11, 9, 12, 9, 8, 13, 9, 8, 13, 10, 11, 14, 11, 8, 13, 12, 10, 13, 9, 9, 16, 10, 11, 14, 10, 10, 15, 10, 9, 16, 12, 9, 16, 12, 11, 18 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Conjecture: For all n, a(n) > 0; a(n) > A002375(n).

LINKS

Table of n, a(n) for n=1..90.

Eric Weisstein's World of Mathematics, Goldbach Conjecture

Wikipedia, Goldbach's conjecture

Wikipedia, Waring-Goldbach problem

Index entries for sequences related to Goldbach conjecture

EXAMPLE

a(1) = #{1+1} = 1; a(2) = #{1+3} = 1; a(3) = #{1+5, 3+3} = 2;

a(20) = #{3+37, 3^2+31, 11+29, 13+3^3, 17+23} = 5;

a(21) = #{1+41, 5+37, 11+31, 13+29, 17+5^2, 19+23} = 6.

MAPLE

isA061345 := proc(n)

    if n = 1 then

        true;

    elif type(n, 'even') then

        false;

    elif nops(numtheory[factorset](n)) = 1 then

        true;

    else

        false;

    end if;

end proc:

A117119 := proc(n)

    local a, j, i;

    a := 0 ;

    for i from 1 do

        j := 2*n-i ;

        if j < i then

            break;

        end if;

        if isA061345(i) and isA061345(j) then

            a := a+1 ;

        end if;

    end do:

    a ;

end proc:

seq(A117119(n), n=1..60) ; # R. J. Mathar, Jul 09 2016

MATHEMATICA

oppQ[n_] := n == 1 || OddQ[n] && PrimeNu[n] == 1; a[n_] := (k = 0; For[i = 1, True, i++, j = 2n - i; If[j < i, Break[]]; If[oppQ[i] && oppQ[j], k++] ]; k); Array[a, 100] (* Jean-Fran├žois Alcover, Feb 13 2018 *)

CROSSREFS

Cf. A061345.

Sequence in context: A196048 A176075 A256555 * A208280 A139141 A122953

Adjacent sequences:  A117116 A117117 A117118 * A117120 A117121 A117122

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, Apr 15 2006

STATUS

approved

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Last modified July 31 13:25 EDT 2021. Contains 346373 sequences. (Running on oeis4.)