A163457 a(n) = the smallest divisor of n such that this and all greater divisors of n are non-coprime to each other.

2, 3, 2, 5, 3, 7, 2, 3, 5, 11, 4, 13, 7, 5, 2, 17, 3, 19, 5, 7, 11, 23, 4, 5, 13, 3, 7, 29, 6, 31, 2, 11, 17, 7, 6, 37, 19, 13, 8, 41, 7, 43, 11, 9, 23, 47, 4, 7, 5, 17, 13, 53, 3, 11, 8, 19, 29, 59, 6, 61, 31, 9, 2, 13, 11, 67, 17, 23, 10, 71, 9, 73, 37, 5, 19, 11, 13, 79, 8, 3, 41, 83, 12, 17

Offset

2,1

Links

Alois P. Heinz, Table of n, a(n) for n = 2..5000

Example

The divisors of 30 are 1,2,3,5,6,10,15,30. 5 is coprime to 6, so a(30) >= 6. Checking the greatest common divisors of all pairs of distinct divisors >= 6: GCD(6,30)=6, GCD(6,15)=3, GCD(6,10)=2, GCD(10,30)=10, GCD(10,15)=5, and GCD(15,30) = 15. Since all of these GCD's are >= 2, then a(30) = 6.

Maple

with(numtheory): a:= proc(n) local l, j, m, s, h, k; l:= sort([divisors(n) []]); m:= nops(l); h:= m; s:= 1; k:= m; do for j from k to s by -1 do if igcd (l[k], l[j])>1 then h:=j else break fi od; s:= h; k:= k-1; if k<s then break fi od; l[s] end: seq (a(n), n=2..100); # Alois P. Heinz, Aug 03 2009

Mathematica

a[n_] := Module[{dd = Divisors[n], selQ}, selQ[d_] := Module[{sd = Select[ dd, # >= d&]}, FreeQ[GCD@@@Subsets[sd, {2}], 1]]; SelectFirst[dd, selQ]];
a /@ Range[2, 100] (* Jean-François Alcover, Nov 20 2020 *)

Crossrefs

Cf. A162325.

Sequence in context: A109395 A145254 A379120 * A285708 A072593 A348907

Adjacent sequences: A163454 A163455 A163456 * A163458 A163459 A163460

Keyword

nonn

Author

Leroy Quet, Jul 28 2009

Extensions

More terms from Alois P. Heinz, Aug 03 2009

Status

approved