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A103840
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Number of ways to represent n as a sum of b^e with b >= 2, e >= 2, e distinct.
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1
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1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 2, 1, 0, 0, 1, 0, 0, 0, 2, 2, 0, 1, 1, 0, 0, 1, 2, 2, 0, 0, 3, 0, 0, 0, 2, 2, 0, 2, 2, 0, 0, 1, 2, 3, 0, 0, 4, 0, 0, 0, 2, 3, 0, 2, 2, 0, 0, 2, 4, 3, 0, 0, 5, 0, 0, 0, 3, 4, 0, 2, 3, 0, 0, 2, 5, 5, 0, 0, 5, 1, 0, 0, 3, 7, 1, 3, 3, 1, 0, 2, 5, 5, 1, 0, 7, 0, 0, 0, 3
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,17
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COMMENTS
| 291 is the largest number that cannot be expressed in this way.
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FORMULA
| G.f.: Prod(e >= 2, 1 + Sum(b >= 2, x^(b^e))).
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EXAMPLE
| 68 = 2^2+4^3 = 2^2+2^6 = 3^2+3^3+2^5 = 5^2+3^3+2^4 = 6^2+2^5 so a(68) = 5. Note that although 4^3 = 2^6, the exponents are different and so 2^2+4^3 and 2^2+2^6 are counted as distinct.
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CROSSREFS
| Cf. A103841 (where a(n) = 0), A103843 (positions of records).
Sequence in context: A186714 A160382 A081221 * A066301 A046660 A183094
Adjacent sequences: A103837 A103838 A103839 * A103841 A103842 A103843
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KEYWORD
| nonn
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AUTHOR
| Gordon Hamilton (hamiltonian(AT)shaw.ca), Mar 29 2005
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EXTENSIONS
| More terms from David W. Wilson (davidwwilson(AT)comcast.net), Mar 30 2005
More terms from David Wasserman (dwasserm(AT)earthlink.net), Apr 24 2008
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