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A282947
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Number of ways of writing n as a sum of a perfect power and a squarefree semiprime.
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2
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0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 2, 2, 1, 0, 2, 2, 0, 0, 3, 3, 1, 1, 2, 1, 0, 1, 4, 3, 0, 1, 2, 3, 1, 3, 3, 3, 2, 2, 7, 3, 1, 0, 4, 5, 2, 2, 3, 3, 1, 2, 3, 4, 1, 1, 4, 5, 3, 2, 4, 4, 3, 3, 6, 3, 0, 2, 6, 6, 0, 4, 4, 3, 1, 1, 7, 1, 1, 2, 5, 5, 2, 4, 4, 6, 2, 3, 6, 4, 2, 3, 6, 6, 4, 3, 4, 4, 2, 5, 6, 5, 3, 1, 3, 5, 0, 3, 6, 3, 3, 2, 6, 5, 3, 1, 5, 7, 5
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OFFSET
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0,15
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COMMENTS
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Conjecture: a(n) > 0 for all n > 108.
Conjecture: a(n) > 1 for all n > 604,
Conjecture: a(n) > 2 for all n > 1008, etc.
First occurrence of k: 0, 7, 14, 22, 30, 47, 66, 42, 127, 138, 150, 222, 251, 303, 210, 430, 330, 462, 670, 770, 983, 878, 1038, 1142, 1355, 1482, ... (End)
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LINKS
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Eric Weisstein's World of Mathematics, Semiprime
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FORMULA
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EXAMPLE
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a(22) = 3 because we have [21, 1], [16, 6] and [14, 8].
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MATHEMATICA
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nmax = 120; CoefficientList[Series[(x + Sum[Boole[GCD @@ FactorInteger[k][[All, 2]] > 1] x^k, {k, 2, nmax}]) (Sum[MoebiusMu[k]^2 Floor[2/PrimeOmega[k]] Floor[PrimeOmega[k]/2] x^k, {k, 2, nmax}]), {x, 0, nmax}], x]
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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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