cp's OEIS Frontend

A213250 Numbers n such that the coefficient of x^n in the expansion of Product_{k>=1} (1-x^k)^2 is zero.

%I A213250 #22 Jul 19 2022 05:46:05
%S A213250 7,11,12,17,18,21,22,25,32,37,39,41,42,43,46,47,49,54,57,58,60,62,65,
%T A213250 67,68,72,74,75,76,81,82,87,88,90,92,95,97,98,99,106,107,109,111,112,
%U A213250 113,116,117,120,122,123,125,126,128,130,132,136,137
%N A213250 Numbers n such that the coefficient of x^n in the expansion of Product_{k>=1} (1-x^k)^2 is zero.
%C A213250 Indices of zero entries in A002107.
%C A213250 Asymptotic density is 1.
%C A213250 Contains A093519, numbers with no representation as sum of two or fewer pentagonal numbers.
%H A213250 Seiichi Manyama, <a href="/A213250/b213250.txt">Table of n, a(n) for n = 1..10000</a>
%t A213250 LongPoly = Series[Product[1 - q^n, {n, 1, 300}]^2, {q, 0, 300}]; ZeroTable = {}; For[i = 1, i < 301, i++, If[Coefficient[LongPoly, q^i] == 0, AppendTo[ZeroTable, i]]]; ZeroTable
%o A213250 (PARI)
%o A213250 x='x+O('x^200);
%o A213250 v=Vec(eta(x)^2 - 1);
%o A213250 for(k=1,#v,if(v[k]==0,print1(k,", ")));
%o A213250 /* _Joerg Arndt_, Jun 07 2012 */
%o A213250 (Julia) # DedekindEta is defined in A000594.
%o A213250 function A213250List(upto)
%o A213250     eta = DedekindEta(upto, 2)
%o A213250     [n - 1 for (n, z) in enumerate(eta) if z == 0] end
%o A213250 println(A213250List(140))  # _Peter Luschny_, Jul 19 2022
%Y A213250 Cf. A002107, A093519.
%Y A213250 Numbers k such that the coefficient of x^k in the expansion of Product_{j>=1} (1 - x^j)^m is zero: A090864 (m=1), this sequence (m=2), A014132 (m=3), A302056 (m=4), A302057 (m=5), A020757 (m=6), A322043 (m=15).
%K A213250 easy,nonn
%O A213250 1,1
%A A213250 _William J. Keith_, Jun 07 2012