A003038 -id:A003038 - cp's OEIS frontend

A126581 Freeman Dyson's list of values of k for which there is an identity of a certain type for the k-th power of the Dedekind eta function.

3, 8, 10, 14, 15, 21, 24, 26, 28, 35, 36, 45, 48, 52, 55, 63, 66, 78, 80, 91, 99, 105, 120, 133, 136, 143, 153, 168, 171, 190, 195, 210, 224, 231, 248, 253, 255, 276, 288, 300, 323, 325, 351, 360, 378, 399, 406, 435, 440, 465, 483, 496, 528, 561, 575, 595, 624, 630

Offset: 1

N. J. A. Sloane, Mar 17 2007

nonn

I. G. Macdonald showed that this list is the same as A003038 except for the presence of the number 26.

Freeman J. Dyson, Missed opportunities, Bull. Amer. Math. Soc. 78 (1972), 635-652.
N. Jacobson, Lie Algebras. Wiley, NY, 1962; pp. 141-146.
I. G. Macdonald, Some conjectures for root systems, SIAM J. Math. Anal., 13 (1982), 988-1007.

Freeman J. Dyson, Missed opportunities, Bull. Amer. Math. Soc. 78 (1972), 635-652.
Wikipedia, Dedekind eta function

Cf. A003038.

Definition clarified by Jonathan Sondow, Mar 24 2013

A001066 Dimensions (sorted, with duplicates removed) of real simple Lie algebras.

Original entry on oeis.org

3, 6, 8, 10, 14, 15, 16, 20, 21, 24, 28, 30, 35, 36, 42, 45, 48, 52, 55, 56, 63, 66, 70, 72, 78, 80, 90, 91, 96, 99, 104, 105, 110, 120, 126, 132, 133, 136, 143, 153, 156, 160, 168, 171, 182, 190, 195, 198, 210, 224, 231, 240, 248, 253, 255, 266, 272, 276, 286, 288, 300, 306

Offset: 1

Richard E. Borcherds (reb(AT)math.berkeley.edu)

The possible dimensions of real simple Lie algebras are the numbers n and 2n where n runs through the dimensions of the complex simple Lie algebras.

			6 is the dimension of the real simple Lie algebra SL_2(C).

Freeman J. Dyson, Missed opportunities, Bull. Amer. Math. Soc. 78 (1972), 635-652.
N. Jacobson, Lie Algebras. Wiley, NY, 1962; see pp. 141-146.

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Cf. A003038.

Subsequences, apart from some initial terms: A000217, A000384, A002378, A005563, A014105.

import Data.Set (deleteFindMin, fromList, insert)
a001066 n = a001066_list !! (n-1)
a001066_list = f (fromList [h, 2 * h]) $ tail a003038_list where
   h = head a003038_list
   f s (x:xs) = m : f (x `insert` (( 2 * x) `insert` s')) xs where
     (m, s') = deleteFindMin s
-- Reinhard Zumkeller, Dec 16 2012

max = 18; sa = Table[k*(k+2), {k, 1, max}]; sb = Table[k*(2k+1), {k, 2, max}]; sd := Table[k*(2k-1), {k, 4, max}]; se = {14, 52, 78, 133, 248}; Select[ Union[sa, 2*sa, sb, 2*sb, sd, 2*sd, se, 2*se], # <= max^2 &] (* Jean-François Alcover, Apr 02 2012, after A003038 *)

Numbers n and 2n as n runs through A003038.

Entry revised by N. J. A. Sloane, Mar 16 2007

cp's OEIS Frontend

A126581 Freeman Dyson's list of values of k for which there is an identity of a certain type for the k-th power of the Dedekind eta function.

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A001066 Dimensions (sorted, with duplicates removed) of real simple Lie algebras.

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