

A146891


Terminal point of a repeated reduction of usigma starting at 2^n.


2



1, 6, 20, 72, 72, 72, 20, 72, 72, 17280, 4800, 17280, 72, 17280, 1152000, 5184, 5184, 5184, 96000, 5184, 345600, 1244160, 320000, 1244160, 82944000, 89579520, 71663616000, 298598400, 1244160, 82944000, 23040000, 82944000, 19906560000
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

0,2


COMMENTS

Let PF_p(n) be the highest power of p dividing n. Examples are PF_2(n) = A006519(n), PF_3(n) = A038500(n) and PF_5(n) = 5^A112765(n) for the cases p = 2, 3, and 5.
Multiindexed PF_(p1,p2,...)(n) are defined as the products PF_(p1)(n)*PF_(p2)(n)*...
For each n, we define an auxiliary sequence b(k) starting at b(0) = 2^n by b(k+1) = A034448(b(k))/PF_(2,3,5)(A034448(b(k)), that is, repeated removal of all powers of 2, 3 and 5 from the unitary sigma value. b(k) terminates at some k with b(k)=1. In addition there is an auxiliary parallel sequence c(k) defined by c(0)=2^n and recursively c(k+1) = c(k)*PF_(3,5)(A034448(b(k)))/A006519(A034448(b(k))), reducing 2^n by the powers of 2 which are divided out of the sequence b.
The sequence is defined by a(n) = c(k), the auxiliary sequence c at the point where b terminates.
All values of the sequence a(n) are 5smooth, i.e., members of A051037.


LINKS

Table of n, a(n) for n=0..32.


EXAMPLE

n=5
b(n) : 2^5 > 11 > 1
c(n) : 2^5 > 2^5*3 > 2^3*3^2
So a(5) = c(2) = 2^3*3^2 = 72.


MAPLE

PF := proc(n, p) local nshf, a ; a := 1; nshf := n ; while (nshf mod p ) = 0 do nshf := nshf/p ; a := a*p ; od: a ; end:
A146891 := proc(n) local b, a, k, t ;
b := [2^n] ;
while op(1, b) <> 1 do
t := A034448(op(1, b)) ;
b := [op(b), t/A006519(t)/ A038500(t)/PF(t, 5) ] ;
od:
a := 2^n ;
for k from 2 to nops(b) do
t := A034448(op(k1, b)) ;
a := a/ A006519(t) *A038500(t)*PF(t, 5) ;
od:
a ;
end:
# R. J. Mathar, Jun 24 2009


CROSSREFS

Cf. A146892, A151659.
Sequence in context: A050930 A074353 A075055 * A235367 A189604 A153372
Adjacent sequences: A146888 A146889 A146890 * A146892 A146893 A146894


KEYWORD

nonn


AUTHOR

Yasutoshi Kohmoto, Apr 17 2009


EXTENSIONS

More terms from R. J. Mathar, Jun 24 2009
Edited by R. J. Mathar, Jul 02 2009
Description of relation between a(n) and c(k) corrected by R. J. Mathar, Jul 07 2009


STATUS

approved



