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 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. Multi-indexed 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 5-smooth, i.e., members of A051037. LINKS 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(k-1, 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

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Last modified September 16 23:53 EDT 2021. Contains 347477 sequences. (Running on oeis4.)