A146892 For definition see comments lines.

1, 6, 6, 72, 72, 72, 6, 72, 72, 5184, 6, 5184, 72, 5184, 31104, 5184, 5184, 5184, 2592, 5184, 432, 373248, 36, 373248, 31104, 26873856, 26873856, 26873856, 373248, 31104, 36, 31104, 2239488, 2239488, 1934917632, 26873856, 31104, 2239488

Offset

0,2

Comments

Let USigma denote the unitary sigma function, A034448.

As in A146891, let PF_p(n) denote the largest power of the prime p dividing n. PF_2 is A006519, and PF_3 is A038500. Furthermore define PF_1(n)=1.

Extension to multi-prime-indices is done by multiplying the corresponding functions: PF_{p,q,..}(n) = PF_p(n)*PF_q(n)*... An example of this is PF_{2,3} = A065331.

[How to compute c(m)]

Case of Base Primes = {2}{3}

c(0)=2^m, b(0)=2^m

c(n)=c(n-1)/PF_2[USigma[b(n-1)]]*PF_3[USigma[b(n-1)]]

b(n)=USigma[b(n-1)]/ PF_2,3[USigma[b(n-1)]]

IF b(k)=1 THEN END

a(m)=c(k)

Sequence gives a(m)

Factorization of term becomes 2^r*3^s.

Links

Table of n, a(n) for n=0..37.

Maple

A146892 := proc(n) local b, a, k ;
   b := [2^n] ;
   while op(-1, b) <> 1 do
       b := [op(b), A065330(A034448(op(-1, b))) ] ;
   od:
   a := 2^n ;
   for k from 2 to nops(b) do
       a := a/ A006519(A034448(op(k-1, b))) *A038500(A034448(op(k-1, b))) ;
   od:
   a ;
end: # R. J. Mathar, Jun 24 2009

Crossrefs

Cf. A146891.

Sequence in context: A269888 A269767 A065239 * A347916 A361738 A320824

Adjacent sequences: A146889 A146890 A146891 * A146893 A146894 A146895

Keyword

nonn,uned

Author

Yasutoshi Kohmoto, Apr 17 2009

Extensions

More terms from R. J. Mathar, Jun 24 2009

Status

approved