login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

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: A039473 A309123 A146170 * A071366 A321517 A045165

Adjacent sequences:  A217854 A217855 A217856 * A217858 A217859 A217860

KEYWORD

nonn

AUTHOR

Michel Marcus, Oct 13 2012

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

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