A217857 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.

50, 75, 98, 18, 70, 75, 338, 12, 245, 50, 75, 455, 722, 63, 20, 98, 50, 50, 63, 147, 475, 30, 182, 385, 1922, 12, 242, 105, 325, 175, 338, 75, 117, 3698, 28, 1463, 363, 50, 310, 45, 75, 935, 98, 147, 12, 507, 242, 325, 245, 105, 7442, 171, 1859, 98, 63, 2365

Offset: 1

Author

Michel Marcus, Oct 13 2012

Keywords

• nonn

Comments

w(n) belongs to A217856, too.

w(20) = 98, w(98) = 63, w(63) = 75, and w(75) = 20.

For every n in A217856, iterating w(n), w(w(n)), ... will lead to this cycle.

Examples

			w(12) = wpqr(2, 2, 3) = gpf(4)*gpf(5)*gpf(5) = 2*5*5 = 50.
w(20) = wpqr(2, 2, 5) = gpf(4)*gpf(7)*gpf(7) = 2*7*7 = 98.
		

Links

• Wushi Goldring, Dynamics of the w function and primes, Journal of Number Theory, Volume 119, Issue 1, July 2006, Pages 86-98.
• Yong-Gao Chen, Ying Shi, Distribution of primes and dynamics of the w function, Journal of Number Theory, Volume 128, Issue 7, July 2008, Pages 2085-2090.

Crossrefs

Cf. A006530, A217856.

Programs

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])), ", "););););}