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A046675
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Expansion of Product_{i>0} (1-x^{p_i}), where p_i are the primes.
(Formerly N0003)
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14
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1, 0, -1, -1, 0, 0, 0, 0, 1, 1, 0, -1, 0, 0, 0, 0, 1, 0, 0, -1, 0, 0, 0, -1, 1, 1, 0, -1, 0, -1, 0, -1, 1, 1, 1, -1, 1, -1, -1, -1, 2, 0, 1, -1, 1, 0, 0, -3, 2, 1, 1, -2, 1, -2, 1, -2, 1, 0, 2, -3, 3, -1, 0, -2, 4, -1, 2, -4, 1, -1, 3, -5, 4, -1, 2, -3, 4, -4, 3, -5, 3, -1, 4, -8, 6, -1, 2, -7, 6, -4, 8, -6, 3
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OFFSET
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0,41
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COMMENTS
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The difference between the number of even partitions of n into distinct primes and the number of odd partitions of n into distinct primes. - T. D. Noe, Sep 08 2006
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REFERENCES
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B. C. Berndt and B. M. Wilson, Chapter 5 of Ramanujan's second notebook, pp. 49-78 of Analytic Number Theory (Philadelphia, 1980), Lect. Notes Math. 899, 1981, see Entry 29.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
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LINKS
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FORMULA
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MATHEMATICA
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CoefficientList[Series[Product[1 - x^Prime[i], {i, 1, 100}], {x, 0, 100}], x] (* Vaclav Kotesovec, Sep 13 2018 *)
nmax = 100; pmax = PrimePi[nmax]; poly = ConstantArray[0, nmax + 1]; poly[[1]] = 1; poly[[2]] = 0; poly[[3]] = -1; Do[p = Prime[k]; Do[poly[[j]] -= poly[[j - p]], {j, nmax + 1, p + 1, -1}]; , {k, 2, pmax}]; poly (* Vaclav Kotesovec, Sep 20 2018 *)
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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