A117365 -id:A117365 - cp's OEIS frontend

A117366 a(n) = smallest prime greater than the largest prime dividing n.

2, 3, 5, 3, 7, 5, 11, 3, 5, 7, 13, 5, 17, 11, 7, 3, 19, 5, 23, 7, 11, 13, 29, 5, 7, 17, 5, 11, 31, 7, 37, 3, 13, 19, 11, 5, 41, 23, 17, 7, 43, 11, 47, 13, 7, 29, 53, 5, 11, 7, 19, 17, 59, 5, 13, 11, 23, 31, 61, 7, 67, 37, 11, 3, 17, 13, 71, 19, 29, 11, 73, 5, 79, 41, 7, 23, 13, 17, 83, 7

Offset: 1

Leroy Quet, Mar 10 2006

nonn

			5 is the largest prime dividing 10. So a(10) is the smallest prime > 5, which is 7.

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Cf. A117364, A117365, A117367.

Cf. A000040, A006530, A151800, A159081.

a117366 = a151800 . a006530  -- Reinhard Zumkeller, Apr 06 2015

Table[Prime[PrimePi[FactorInteger[n][[Length[FactorInteger[n]]]][[1]]]+1], {n, 80}] (* Stefan Steinerberger, Apr 09 2006 *)

A117366(n) = if(1==n, 2, nextprime(1+vecmax(factor(n)[, 1]))); \\ Antti Karttunen, Jan 15 2020

a(n) = A151800(A006530(n)). - Reinhard Zumkeller, Apr 06 2015

a(n) = A000040(A159081(n)). - Antti Karttunen, Jan 15 2020

More terms from Stefan Steinerberger, Apr 09 2006

A117367 a(n) = smallest prime greater than the smallest prime dividing n.

Original entry on oeis.org

2, 3, 5, 3, 7, 3, 11, 3, 5, 3, 13, 3, 17, 3, 5, 3, 19, 3, 23, 3, 5, 3, 29, 3, 7, 3, 5, 3, 31, 3, 37, 3, 5, 3, 7, 3, 41, 3, 5, 3, 43, 3, 47, 3, 5, 3, 53, 3, 11, 3, 5, 3, 59, 3, 7, 3, 5, 3, 61, 3, 67, 3, 5, 3, 7, 3, 71, 3, 5, 3, 73, 3, 79, 3, 5, 3, 11, 3, 83, 3, 5, 3, 89, 3, 7, 3, 5, 3, 97, 3, 11, 3, 5

Offset: 1

Leroy Quet, Mar 10 2006

nonn

All even-indexed terms are 3.

			5 is the smallest prime dividing 35. So a(35) is the smallest prime > 5, which is 7.

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Cf. A117364, A117365, A117366.

with(numtheory): a:=proc(n): if n=1 then 2 else nextprime(factorset(n)[1]) fi: end: seq(a(n),n=1..100); # Emeric Deutsch, Apr 22 2006

Table[NextPrime[FactorInteger[n][[1, 1]]], {n, 93}] (* Michael De Vlieger, Sep 16 2017 *)

More terms from Emeric Deutsch, Apr 22 2006

A117364 a(n) = largest prime less than the largest prime dividing n (or 1 if there is no such prime).

Original entry on oeis.org

1, 1, 2, 1, 3, 2, 5, 1, 2, 3, 7, 2, 11, 5, 3, 1, 13, 2, 17, 3, 5, 7, 19, 2, 3, 11, 2, 5, 23, 3, 29, 1, 7, 13, 5, 2, 31, 17, 11, 3, 37, 5, 41, 7, 3, 19, 43, 2, 5, 3, 13, 11, 47, 2, 7, 5, 17, 23, 53, 3, 59, 29, 5, 1, 11, 7, 61, 13, 19, 5, 67, 2, 71, 31, 3, 17, 7, 11, 73, 3, 2, 37, 79, 5, 13, 41, 23

Offset: 1

Leroy Quet, Mar 10 2006

nonn

a(n) = 1 if and only if n is a power of 2 (including 1).
a(n/3) = 2 iff n/3 is A003586: 3-smooth numbers: numbers of the form 2^i*3^j with i, j >= 0.
a(n/5) = 3 iff n/5 is A051037: 5-smooth numbers: i.e. numbers whose prime divisors are all <= 5, etc.

			5 is the largest prime dividing 10. So a(10) is the largest prime < 5, which is 3.

Cf. A117365, A117366, A117367.

PrevPrime[n_] := Block[{k = n - 1}, While[ ! PrimeQ[k], k-- ]; k]; f[n_] := Block[{k = PrevPrime@ FactorInteger[Max[2, n]][[ -1, 1]]}, If[k > 1, k, 1]]; Array[f, 87] (* Robert G. Wilson v *)

More terms from Robert G. Wilson v, May 01 2006

A117368 a(n) = largest prime less than the smallest prime dividing (2n-1).

Original entry on oeis.org

2, 3, 5, 2, 7, 11, 2, 13, 17, 2, 19, 3, 2, 23, 29, 2, 3, 31, 2, 37, 41, 2, 43, 5, 2, 47, 3, 2, 53, 59, 2, 3, 61, 2, 67, 71, 2, 5, 73, 2, 79, 3, 2, 83, 5, 2, 3, 89, 2, 97, 101, 2, 103, 107, 2, 109, 3, 2, 5, 7, 2, 3, 113, 2, 127, 5, 2, 131, 137, 2, 7, 3, 2, 139, 149, 2, 3, 151, 2, 5, 157, 2

Offset: 2

Leroy Quet, Mar 10 2006

nonn

Placing a 1 between each term of this sequence gets sequence A117365.

			a(13) = 3 because smallest prime dividing 25 is 5 and largest prime less than 5 is 3.

Robert Israel, Table of n, a(n) for n = 2..10000

Cf. A006512, A090368, A117365, A151799.

with(numtheory): a:=proc(n): prevprime(factorset(2*n-1)[1]): end: seq(a(n),n=2..90); # Emeric Deutsch, Apr 22 2006

prs=Prime[Range[50]];
f[n_]:=NextPrime[First[Select[prs,Divisible[2 n-1,#]&]],-1]
f/@Range[2,90]  (* Harvey P. Dale, Jan 23 2011 *)

From Robert Israel, Apr 14 2019: (Start)
a(n) = A151799(A090368(n)).
a(n) = 2*n-3 if 2*n-1 is in A006512. (End)

More terms from Emeric Deutsch, Apr 22 2006

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A117366 a(n) = smallest prime greater than the largest prime dividing n.

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A117367 a(n) = smallest prime greater than the smallest prime dividing n.

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A117364 a(n) = largest prime less than the largest prime dividing n (or 1 if there is no such prime).

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A117368 a(n) = largest prime less than the smallest prime dividing (2n-1).

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