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%I N0003 #48 Aug 17 2020 02:00:15
%S 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,
%T -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,
%U 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
%N Expansion of Product_{i>0} (1-x^{p_i}), where p_i are the primes.
%C 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
%D 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.
%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%H Seiichi Manyama, <a href="/A046675/b046675.txt">Table of n, a(n) for n = 0..10000</a> (terms 0..1000 from T. D. Noe)
%H H. Gupta, <a href="http://www.insa.nic.in/writereaddata/UpLoadedFiles/PINSA/Vol21A_1955_3_Art09.pdf">Partitions into distinct primes</a>, Proc. Nat. Acad. Sci. India, 21 (1955), 185-187 [broken link].
%F a(n) = A184171(n) - A184172(n). - _R. J. Mathar_, Jan 10 2011
%t CoefficientList[Series[Product[1 - x^Prime[i], {i, 1, 100}], {x, 0, 100}], x] (* _Vaclav Kotesovec_, Sep 13 2018 *)
%t 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 *)
%Y Cf. A000607, A000586.
%K sign
%O 0,41
%A _N. J. A. Sloane_
%E Revised by _N. J. A. Sloane_, Jun 10 2012
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