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A071330
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Number of decompositions of n into sum of two prime powers.
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8
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0, 1, 1, 2, 2, 3, 2, 3, 3, 4, 3, 4, 3, 4, 3, 4, 3, 5, 3, 5, 4, 4, 2, 5, 3, 5, 4, 5, 3, 6, 3, 7, 5, 7, 4, 7, 2, 6, 4, 6, 3, 6, 3, 6, 5, 6, 2, 8, 3, 8, 4, 6, 2, 9, 3, 7, 4, 6, 2, 8, 3, 7, 4, 7, 3, 9, 2, 8, 5, 7, 2, 10, 3, 8, 6, 7, 3, 9, 2, 9, 4, 7, 4, 11, 3, 9, 4, 7, 3, 12, 4, 8, 3, 7, 2
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OFFSET
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1,4
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COMMENTS
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a(2*n) > 0 (Goldbach's conjecture).
a(A071331(n)) = 0; A095840(n) = a(A000961(n)).
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..10000
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EXAMPLE
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10 = 1+3^2 = 2+2^3 = 3+7 = 5+5, therefore a(10) = 4;
11 = 2+3^2 = 3+2^3 = 4+7, therefore a(11) = 3;
12 = 1+11 = 3+3^2 = 2^2+2^3 = 5+7, therefore a(12) = 4;
a(149)=0, as for all x<149: if x prime power then 149-x not.
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MATHEMATICA
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primePowerQ[n_] := Length[ FactorInteger[n]] == 1; a[n_] := (r = 0; Do[ If[ primePowerQ[k] && primePowerQ[n-k], r++], {k, 1, Floor[n/2]}]; r); Table[a[n], {n, 1, 95}](* From Jean-François Alcover, Nov 17 2011, after Michael Porter *)
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PROG
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Contribution from Michael B. Porter, Dec 04 2009: (Start)
(PARI) ispp(n) = (omega(n)==1 || n==1)
A071330(n) = {local(r); r=0; for(i=1, floor(n/2), if(ispp(i) && ispp(n-i), r++)); r} (End)
(Haskell)
a071330 n = sum $
map (a010055 . (n -)) $ takeWhile (<= n `div` 2) a000961_list
-- Reinhard Zumkeller, Jan 11 2013
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CROSSREFS
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Cf. A000961, A002375, A071331.
Cf. A061358, A109829.
Cf. A010055.
Sequence in context: A182745 A129843 A050430 * A092333 A107452 A205018
Adjacent sequences: A071327 A071328 A071329 * A071331 A071332 A071333
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KEYWORD
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nonn,nice
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AUTHOR
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Reinhard Zumkeller, May 19 2002
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STATUS
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approved
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