accident?

[y.kohmoto]

    I wonder why my sequence looks like A050354.
    Is there any explanation about this phenomenon?

    Yasutoshi

         --------------------

ID Number: A051707
Sequence:  1,1,1,3,1,5,1,8,3,5,1,21,1,5,5,23,1,21,1,21
Name:      Number of factorizations of (n,n) into pairs (k,l).
Comments:  Pairs (k,l) must satisfy 0<k, 0<l; if k=1 then l=1. Definition of
              "*": (a,b)*(x,y)=(a*x,b*y); unit is (1,1).
           a(n) depends only on prime signature of n
Example:   (6,6)=(2,1)*(3,6)=(2,6)*(3,1)=(2,2)*(3,3)=(2,3)*(3*2), so
              a(6)=5.See also:  Cf. A025487, A050354.
Keywords:  nonn,nice,easy,more
Offset:    1
Author(s): Yasutoshi Kohmoto (kohmoto(AT)z2.zzz.or.jp)



ID Number: A050354
Sequence:  1,1,1,3,1,5,1,9,3,5,1,21,1,5,5,27,1,21,1,21,5,5,1,81,3,5,9,
           21,1,37,1,81,5,5,5,111,1,5,5,81,1,37,1,21,21,5,1,297,3,21,5,
           21,1,81,5,81,5,5,1,201,1,5,21,243,5,37,1,21,5,37,1,513,1,5,
           21,21,5,37,1,297,27,5,1,201
Name:      Ordered factorizations of n with one level of parentheses.
Comments:  a(n) depends only on prime signature of n (cf. A025487). So a(24)
=
              a(375) since 24=2^3*3 and 375=3*5^3 both have prime signature
(3,1).
Formula:   Dirichlet g.f.: (2-zeta(s))/(3-2*zeta(s)).
Example:   6=(6)=(3*2)=(2*3)=(3)*(2)=(2)*(3).
See also:  Cf. A002033, A050351-A050359. a(p^k)=3^(k-1).
              a(A002110)=A050351.Keywords:  nonn
Offset:    1
Author(s): Christian G. Bower (bowerc(AT)usa.net), Oct 15 1999.

    to Robert and Hugo :
    Thanks for the extension for A083140.