A233570 Replace the smallest prime factor p in n (if any) with the prime following p.

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

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: A346125 A320472 A064802 * A181766 A047584 A229089

Adjacent sequences: A233567 A233568 A233569 * A233571 A233572 A233573

Keyword

nonn

Author

Stanislav Sykora, Dec 13 2013

Status

approved