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A196228
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Number of ways of writing n as sum of a prime and a perfect power.
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3
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0, 0, 1, 1, 0, 2, 1, 1, 1, 1, 3, 2, 1, 2, 2, 1, 1, 2, 2, 2, 3, 1, 2, 1, 1, 1, 4, 2, 2, 3, 1, 4, 2, 2, 3, 1, 2, 5, 4, 2, 2, 2, 2, 3, 4, 2, 3, 2, 3, 2, 4, 2, 2, 3, 3, 4, 2, 1, 2, 2, 2, 4, 3, 1, 2, 3, 3, 5, 4, 2, 2, 3, 2, 2, 5, 1, 4, 2, 3, 4, 2, 1, 5, 3, 1, 4, 4
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OFFSET
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1,6
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COMMENTS
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In this case, perfect power does not include 0.
Different from A133364. The first difference is at n=74, where a(n) = 2 but A133364(n) = 3.
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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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FORMULA
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a(n) = Card_{n=i+j where i is in A000040 and j is in A001597}.
G.f.: (Sum_{k>=1} x^prime(k))*(Sum_{k = i^j, i>=1, j>=2} x^k). - Ilya Gutkovskiy, Feb 18 2017
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EXAMPLE
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a(1) = a(2) = a(5) = a(1549) = a(1771561) = 0, see A119748.
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MATHEMATICA
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nn = 100; pwrs = Union[{1}, Flatten[Table[Range[2, Floor[nn^(1/ex)]]^ex, {ex, 2, Floor[Log[2, nn]]}]]]; pp = Prime[Range[PrimePi[nn]]]; t = Table[0, {nn}]; Do[ t[[i[[1]]]] = i[[2]], {i, Tally[Sort[Select[Flatten[Outer[Plus, pwrs, pp]], # <= nn &]]]}]; t (* T. D. Noe, Sep 29 2011 *)
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CROSSREFS
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Cf. A119748 (zero terms).
Cf. A000040, A001597, A133364.
Sequence in context: A212171 A337255 A337375 * A133364 A063420 A347917
Adjacent sequences: A196225 A196226 A196227 * A196229 A196230 A196231
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KEYWORD
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easy,nonn
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AUTHOR
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Philippe Deléham, Sep 29 2011
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EXTENSIONS
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Edited by Franklin T. Adams-Watters, Sep 29 2011
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STATUS
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approved
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