A106403 -id:A106403 - cp's OEIS frontend

A005776 Exponents m_i associated with Weyl group W(E_8).

Original entry on oeis.org

1, 7, 11, 13, 17, 19, 23, 29

Offset: 1

N. J. A. Sloane

Numbers coprime to 30 in that number's reduced residue system. - Alonso del Arte, Oct 03 2017

H. S. M. Coxeter and W. O. J. Moser, Generators and Relations for Discrete Groups, 4th ed., Springer-Verlag, NY, reprinted 1984, p. 141.

Abel Jansma, E_8 Symmetry Structures in the Ising model, Master's thesis, University of Amsterdam, 2018.
Index entries for sequences related to groups.

Cf. A005556 (E_6), A005763 (E_7), A106373, A106374, A106403, A048597.

Exponents(RootDatum("E8")); // Sergei Haller (sergei(AT)sergei-haller.de), Dec 21 2006

Select[Range[30], GCD[30, #] == 1 &] (* Alonso del Arte, Oct 03 2017 *)

select(n->gcd(n,30)==1, [1..29]) \\ Charles R Greathouse IV, Oct 17 2017

A106373 Primitive exponents of the Weyl group W(E_6).

Original entry on oeis.org

3, 9, 11, 15, 17, 23

Offset: 1

N. J. A. Sloane, May 30 2005

C. Chevalley, The Betti numbers of the exceptional Lie groups, pp. 21-24 of Proc. Internat Congress Math., Cambridge 1950, Amer. Math. Soc., 1952.

Cf. A106374, A106403, A005556, A005763, A005776.

Equals 2*A005556(n) + 1.

A106374 Primitive exponents of the Weyl group W(E_7).

Original entry on oeis.org

3, 11, 15, 19, 23, 27, 35

Offset: 1

N. J. A. Sloane, May 30 2005

C. Chevalley, The Betti numbers of the exceptional Lie groups, pp. 21-24 of Proc. Internat Congress Math., Cambridge 1950, Amer. Math. Soc., 1952.

Cf. A106373, A106403, A005556, A005763, A005776.

Equals 2*A005763(n) + 1.

A109161 Triangle read by rows: T(n, k) = n*(n+9) + k + 5, with T(0, 0) = 5 and T(1, 0) = 15.

Original entry on oeis.org

5, 15, 16, 27, 28, 29, 41, 42, 43, 44, 57, 58, 59, 60, 61, 75, 76, 77, 78, 79, 80, 95, 96, 97, 98, 99, 100, 101, 117, 118, 119, 120, 121, 122, 123, 124, 141, 142, 143, 144, 145, 146, 147, 148, 149, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205

Offset: 1

Roger L. Bagula, May 06 2007

			Triangle begins as:
   5;
  15, 16;
  27, 28, 29;
  41, 42, 43, 44;
  57, 58, 59, 60, 61;
  75, 76, 77, 78, 79, 80;

G. C. Greubel, Rows n=0..100 of the triangle, flattened
S. Helgason, A Centennial: Wilhelm Killing and the Exceptional Groups, Mathematical Intelligencer 12, no. 3 (1990). [See p. 3.]

Cf. A106373, A106374, A106403.

T[n_, k_]:= If[n==0 && k==0, 5, If[k==0 && n==1, 15, n*(n+9) +k +5]];
Table[T[n, k], {n, 0, 12}, {k, 0, n}]//Flatten

@CachedFunction
def T(n, k):
    if (n==0 and k==0): return 5
    elif (k==0 and n==1): return 15
    else: return n*(n + 9) + k + 5
flatten([[T(n,k) for k in (0..n)] for n in (0..12)]) # G. C. Greubel, Feb 05 2021

T(n, k) = n*(n+9) + k + 5, with T(0, 0) = 5 and T(1, 0) = 15.

More terms and edits by G. C. Greubel, Feb 05 2021

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A005776 Exponents m_i associated with Weyl group W(E_8).

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A106373 Primitive exponents of the Weyl group W(E_6).

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A106374 Primitive exponents of the Weyl group W(E_7).

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A109161 Triangle read by rows: T(n, k) = n*(n+9) + k + 5, with T(0, 0) = 5 and T(1, 0) = 15.

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