C. Kenneth Fan has authored 2 sequences.
A334802
Positive integers of the form x^4 - y^4 that have exactly 4 divisors.
Original entry on oeis.org
15, 65, 671, 3439, 12209, 102719, 113521, 178991, 246559, 515201, 1124111, 1342879, 2964961, 3940399, 9951391, 21254449, 27220159, 34209169, 45259649, 48986321, 70710641, 92110289, 93084991, 125620111, 131687681, 144402721, 201792079, 211782751, 276694241
Offset: 1
2^4 - 1^4 = 15 = 3*5 and (3, 4, 5) is a Pythagorean triple, so 15 is a term.
6^4 - 5^4 = 671 = 11*61 and (11, 60, 61) is a Pythagorean triple, so 671 is a term.
-
f:= proc(y) if isprime(2*y+1) and isprime(2*y^2 + 2*y+1) then (2*y+1)*(2*y^2+2*y+1) fi end proc:
map(f, [$1..1000]); # Robert Israel, Jun 16 2020
-
Select[(#^4 - (#-1)^4) & /@ Range[420], DivisorSigma[0, #] == 4 &] (* Giovanni Resta, May 12 2020 *)
A007851
Number of elements w of the Weyl group D(n) such that the roots sent negative by w span an Abelian subalgebra of the Lie algebra.
Original entry on oeis.org
1, 4, 14, 48, 167, 593, 2144, 7864, 29171, 109173, 411501, 1560089, 5943199, 22732739, 87253604, 335897864, 1296447899, 5015206349, 19439895089, 75487384829, 293595204239, 1143532045499, 4459774977449, 17413705988873
Offset: 1
C. Kenneth Fan [ ckfan(AT)MIT.EDU ]
- Boothby, T.; Burkert, J.; Eichwald, M.; Ernst, D. C.; Green, R. M.; Macauley, M. On the cyclically fully commutative elements of Coxeter groups, J. Algebr. Comb. 36, No. 1, 123-148 (2012), Table 1 FC Type D.
- C. K. Fan, A Hecke algebra quotient and some combinatorial applications, J. Algebraic Combin. 5 (1996), no. 3, 175-189.
- C. K. Fan, Structure of a Hecke algebra quotient, J. Amer. Math. Soc. 10 (1997), no. 1, 139-167.
- J. R. Stembridge, Some combinatorial aspects of reduced words in finite Coxeter groups, Trans. Amer. Math. Soc. 349 (1997), no. 4, 1285-1332.
Comments