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A213250
Numbers n such that the coefficient of x^n in the expansion of Product_{k>=1} (1-x^k)^2 is zero.
8
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
OFFSET
1,1
COMMENTS
Indices of zero entries in A002107.
Asymptotic density is 1.
Contains A093519, numbers with no representation as sum of two or fewer pentagonal numbers.
LINKS
MATHEMATICA
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
PROG
(PARI)
x='x+O('x^200);
v=Vec(eta(x)^2 - 1);
for(k=1, #v, if(v[k]==0, print1(k, ", ")));
/* Joerg Arndt, Jun 07 2012 */
(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
println(A213250List(140)) # Peter Luschny, Jul 19 2022
CROSSREFS
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).
Sequence in context: A195608 A228523 A193301 * A226689 A117610 A176173
KEYWORD
easy,nonn
AUTHOR
William J. Keith, Jun 07 2012
STATUS
approved