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 A046675 Expansion of Product_{i>0} (1-x^{p_i}), where p_i are the primes. (Formerly N0003) 12
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,41 COMMENTS 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 REFERENCES 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). LINKS Seiichi Manyama, Table of n, a(n) for n = 0..10000 (terms 0..1000 from T. D. Noe) H. Gupta, Partitions into distinct primes, Proc. Nat. Acad. Sci. India, 21 (1955), 185-187 [broken link]. FORMULA a(n) = A184171(n) - A184172(n). - R. J. Mathar, Jan 10 2011 MATHEMATICA 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 *) CROSSREFS Cf. A000607, A000586. Sequence in context: A213726 A116929 A059984 * A275949 A090418 A322452 Adjacent sequences:  A046672 A046673 A046674 * A046676 A046677 A046678 KEYWORD sign AUTHOR EXTENSIONS Revised by N. J. A. Sloane, Jun 10 2012 STATUS approved

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Last modified May 15 10:54 EDT 2021. Contains 343909 sequences. (Running on oeis4.)