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%I #9 Oct 17 2012 13:08:38
%S 50,75,98,18,70,75,338,12,245,50,75,455,722,63,20,98,50,50,63,147,475,
%T 30,182,385,1922,12,242,105,325,175,338,75,117,3698,28,1463,363,50,
%U 310,45,75,935,98,147,12,507,242,325,245,105,7442,171,1859,98,63,2365
%N w(n) = w(pqr) = Gpf(p + q)*Gpf(p + r)*Gpf(q + r), defined when n belongs to A217856, with Gpf(m): greatest prime dividing m.
%C w(n) belongs to A217856, too.
%C w(20) = 98, w(98) = 63, w(63) = 75, and w(75) = 20.
%C For every n in A217856, iterating w(n), w(w(n)), ... will lead to this cycle.
%H Wushi Goldring, <a href="http://dx.doi.org/10.1016/j.jnt.2005.10.010">Dynamics of the w function and primes</a>, Journal of Number Theory, Volume 119, Issue 1, July 2006, Pages 86-98.
%H Yong-Gao Chen, Ying Shi, <a href="http://dx.doi.org/10.1016/j.jnt.2008.02.003">Distribution of primes and dynamics of the w function</a>, Journal of Number Theory, Volume 128, Issue 7, July 2008, Pages 2085-2090.
%e w(12) = wpqr(2, 2, 3) = gpf(4)*gpf(5)*gpf(5) = 2*5*5 = 50.
%e w(20) = wpqr(2, 2, 5) = gpf(4)*gpf(7)*gpf(7) = 2*7*7 = 98.
%o (PARI) gpf(n) = {local(f);if (n==1, return (1));f = factor(n); return (f[length(f~), 1]);} wpqr(p, q, r) = {return (gpf(p+q)*gpf(p+r)*gpf(q+r));} allwf(n) = {for (i=2, n,f = factor(i); len = length(f~);if (len > 1,s = sum(j=1, len, f[j,2]);if (s == 3,print1(wpqr(f[1,1], f[2,1], i/(f[1,1]*f[2,1])), ", "););););}
%Y Cf. A006530, A217856.
%K nonn
%O 1,1
%A _Michel Marcus_, Oct 13 2012
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