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A284171
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Number of partitions of n into distinct perfect powers (including 1).
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4
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1, 1, 0, 0, 1, 1, 0, 0, 1, 2, 1, 0, 1, 2, 1, 0, 1, 2, 1, 0, 1, 2, 1, 0, 1, 3, 2, 1, 2, 3, 2, 1, 2, 3, 3, 2, 4, 5, 3, 2, 4, 5, 3, 2, 4, 6, 4, 2, 4, 7, 5, 2, 5, 8, 5, 2, 5, 8, 6, 3, 5, 10, 8, 4, 6, 10, 8, 4, 6, 10, 9, 5, 7, 11, 10, 6, 8, 12, 10, 6, 8, 13, 11, 7, 9, 15, 13, 7, 10, 16, 14, 8, 10, 16, 15, 9, 10, 17, 16, 9, 11
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OFFSET
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0,10
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COMMENTS
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Differs from the sequence A112345 which does not consider 1 as a perfect power.
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LINKS
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FORMULA
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G.f.: Product_{k>=1} (1 + x^A001597(k)).
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EXAMPLE
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a(25) = 3 because we have [25], [16, 9] and [16, 8, 1].
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MATHEMATICA
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nmax = 100; CoefficientList[Series[(1 + x) Product[(1 + Boole[GCD @@ FactorInteger[k][[All, 2]] > 1] x^k), {k, 1, nmax}], {x, 0, nmax}], x]
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PROG
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(PARI) Vec((1 + x) * prod(k=1, 100, 1 + (gcd(factorint(k)[, 2])>1)*x^k) + O(x^101)) \\ Indranil Ghosh, Mar 21 2017
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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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