OFFSET
1,1
COMMENTS
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
KEYWORD
nonn
AUTHOR
Michel Marcus, Oct 13 2012
STATUS
approved