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a(n) = limiting ratio of successive terms in the trajectory of 1 under the map m -> n*phi(m).
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%I #6 Mar 12 2016 22:29:38

%S 1,1,1,2,2,2,2,4,3,4,4,4,4,4,4,8,8,6,6,8,6,8,8,8,10,8,9,8,8,8,8,16,8,

%T 16,8,12,12,12,12,16,16,12,12,16,12,16,16,16,14,20,16,16,16,18,20,16,

%U 18,16,16,16,16,16,18,32,16,16,16,32,16,16,16,24,24,24,20,24,16,24,24,32,27

%N a(n) = limiting ratio of successive terms in the trajectory of 1 under the map m -> n*phi(m).

%C Let c(1)=1 and c(k+1)=n*phi(c(k)). Then c(k+1)/c(k) is a decreasing sequence of integers, so eventually becomes constant. a(n) is the ratio between terms once that becomes constant. (In fact, as soon as a ratio repeats, it remains constant from that point on.)

%F If p prime, a(p)=a(p-1). If every prime divisor of m divides n, a(n*m)=a(n)*m.

%e For n=25, the sequence m -> n*phi(m) is 1,25,500,5000,50000,...; the ratios are 25,20,10,10,...; so a(25)=10.

%Y Cf. A000010.

%K easy,nonn

%O 1,4

%A _Franklin T. Adams-Watters_, Sep 19 2005

%E Definition revised by _N. J. A. Sloane_, Mar 12 2016