

A233570


Replace the smallest prime factor p in n (if any) with the prime following p.


2



1, 3, 5, 6, 7, 9, 11, 12, 15, 15, 13, 18, 17, 21, 25, 24, 19, 27, 23, 30, 35, 33, 29, 36, 35, 39, 45, 42, 31, 45, 37, 48, 55, 51, 49, 54, 41, 57, 65, 60, 43, 63, 47, 66, 75, 69, 53, 72, 77, 75, 85, 78, 59, 81, 77, 84, 95, 87, 61, 90, 67, 93, 105, 96, 91, 99, 71, 102, 115, 105, 73, 108, 79
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,2


COMMENTS

This endomorphism a:N>N replaces the smallest prime factor in n with the prime following it. For coherence, a(1)=1. Some interesting properties: a(n)>=n, with 1 being the only invariant element, bigomega(a(n)) = bigomega(n), the orbits of all numbers m having the largest prime factor p are congruent with p^bigomega(m); etc.


LINKS

Stanislav Sykora, Table of n, a(n) for n = 1..10000
S. Sykora, PARI scripts: PrimesRelatedFunctions


EXAMPLE

a(21)=a(3*7)=5*7=35.


PROG

(PARI) A233570(n)={local(p); p=SmallestPrimeFactor(n); return
((n\p)*FollowingPrime(p))} \\ See the links for the auxiliary scripts


CROSSREFS

Cf. A000040 (primes), A233511.
Sequence in context: A285627 A320472 A064802 * A181766 A047584 A229089
Adjacent sequences: A233567 A233568 A233569 * A233571 A233572 A233573


KEYWORD

nonn


AUTHOR

Stanislav Sykora, Dec 13 2013


STATUS

approved



