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A117119
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Number of partitions of 2*n into two odd prime powers.
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1
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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
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OFFSET
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1,3
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COMMENTS
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Conjecture: For all n, a(n) > 0; a(n) > A002375(n).
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LINKS
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EXAMPLE
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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.
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MAPLE
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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:
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:
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MATHEMATICA
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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-François Alcover, Feb 13 2018 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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