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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: A284852 A285627 A064802 * A181766 A047584 A229089

Adjacent sequences:  A233567 A233568 A233569 * A233571 A233572 A233573

KEYWORD

nonn

AUTHOR

Stanislav Sykora, Dec 13 2013

STATUS

approved

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Last modified February 24 12:59 EST 2018. Contains 299623 sequences. (Running on oeis4.)