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A213250
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Numbers n such that the coefficient of x^n in the expansion of Product_{k>=1} (1-x^k)^2 is zero.
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8
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7, 11, 12, 17, 18, 21, 22, 25, 32, 37, 39, 41, 42, 43, 46, 47, 49, 54, 57, 58, 60, 62, 65, 67, 68, 72, 74, 75, 76, 81, 82, 87, 88, 90, 92, 95, 97, 98, 99, 106, 107, 109, 111, 112, 113, 116, 117, 120, 122, 123, 125, 126, 128, 130, 132, 136, 137
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OFFSET
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1,1
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COMMENTS
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Indices of zero entries in A002107.
Asymptotic density is 1.
Contains A093519, numbers with no representation as sum of two or fewer pentagonal numbers.
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LINKS
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MATHEMATICA
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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
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PROG
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(PARI)
x='x+O('x^200);
v=Vec(eta(x)^2 - 1);
for(k=1, #v, if(v[k]==0, print1(k, ", ")));
(Julia) # DedekindEta is defined in A000594.
function A213250List(upto)
eta = DedekindEta(upto, 2)
[n - 1 for (n, z) in enumerate(eta) if z == 0] end
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CROSSREFS
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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).
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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