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

1,1

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

Table of n, a(n) for n=1..56.

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: A309123 A146170 A367708 * A071366 A321517 A045165

Adjacent sequences: A217854 A217855 A217856 * A217858 A217859 A217860

Keyword

nonn

Author

Michel Marcus, Oct 13 2012

Status

approved