A162325 a(n) = the largest divisor of n such that this and every smaller divisor of n are all coprime to each other.

1, 2, 3, 2, 5, 3, 7, 2, 3, 5, 11, 3, 13, 7, 5, 2, 17, 3, 19, 2, 7, 11, 23, 3, 5, 13, 3, 2, 29, 5, 31, 2, 11, 17, 7, 3, 37, 19, 13, 2, 41, 3, 43, 2, 5, 23, 47, 3, 7, 5, 17, 2, 53, 3, 11, 2, 19, 29, 59, 3, 61, 31, 7, 2, 13, 3, 67, 2, 23, 7, 71, 3, 73, 37, 5, 2, 11, 3, 79, 2, 3, 41, 83, 3, 17, 43, 29

Offset

1,2

Comments

a(n) = a prime for every n >= 2.

Links

Table of n, a(n) for n=1..87.

Example

The divisors of 28 are 1,2,4,7,14,28. Since 4 is not coprime with 2, but 2 is coprime with 1, then a(28) = 2.

Maple

with(numtheory): a:= proc(n) local l, j, s, h, k; l:= sort([divisors(n)[]]); s:= nops(l); for k while k<=s do h:= k; for j from k+1 to s do if igcd(l[k], l[j])=1 then h:=j else break fi od; s:= h od; l[s] end: seq(a(n), n=1..100); # Alois P. Heinz, Aug 04 2009

Mathematica

a[n_] := Module[{l = Divisors[n], j, s, h, k}, s = Length[l]; For[k = 1, k <= s, k++, h = k; For[j = k + 1, j <= s, j++, If[GCD[l[[k]], l[[j]]] == 1, h = j, Break[]]]; s = h]; l[[s]]];
Array[a, 100] (* Jean-François Alcover, Nov 20 2020, after Alois P. Heinz *)

Crossrefs

Sequence in context: A273283 A359612 A276440 * A324371 A197862 A006530

Adjacent sequences: A162322 A162323 A162324 * A162326 A162327 A162328

Keyword

nonn

Author

Leroy Quet, Jul 01 2009, Jul 23 2009

Extensions

More terms from Alois P. Heinz, Aug 04 2009

Status

approved