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 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. 1
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 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. 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. EXAMPLE 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. PROG (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])), ", "); ); ); ); } CROSSREFS Cf. A006530, A217856. Sequence in context: A039473 A309123 A146170 * A071366 A321517 A045165 Adjacent sequences:  A217854 A217855 A217856 * A217858 A217859 A217860 KEYWORD nonn AUTHOR Michel Marcus, Oct 13 2012 STATUS approved

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Last modified April 12 18:58 EDT 2021. Contains 342932 sequences. (Running on oeis4.)