A213250 - OEIS

A213250

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

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

(list; graph; refs; listen; history; text; internal format)

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

Seiichi Manyama, Table of n, a(n) for n = 1..10000

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

Cf. A002107, A093519.

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

Adjacent sequences: A213247 A213248 A213249 * A213251 A213252 A213253

KEYWORD

easy,nonn

AUTHOR

William J. Keith, Jun 07 2012

STATUS

approved