A160400 a(n) is the smallest positive integer such that a(n)*n = j^k, for some j (j>=1) and k (k>=2).

1, 2, 3, 1, 5, 6, 7, 1, 1, 10, 11, 3, 13, 14, 15, 1, 17, 2, 19, 5, 21, 22, 23, 6, 1, 26, 1, 7, 29, 30, 31, 1, 33, 34, 35, 1, 37, 38, 39, 10, 41, 42, 43, 11, 5, 46, 47, 3, 1, 2, 51, 13, 53, 4, 55, 14, 57, 58, 59, 15, 61, 62, 7, 1, 65, 66, 67, 17, 69, 70, 71, 2, 73, 74, 3, 19, 77, 78, 79, 5

Offset: 1

Author

Leroy Quet, May 12 2009

Keywords

• nonn

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A087320, A001597, A007913.

Programs

Maple

isA001597 := proc(n) local e,p ; if n = 1 then RETURN(true) ; fi; p := [] ; for e in ifactors(n)[2] do p := [op(p), op(2,e) ] ; od: if igcd(op(p)) > 1 then true; else false; fi; end: A160400 := proc(n) local a; for a from 1 do if isA001597(a*n) then RETURN(a) ; fi; od: end: seq(A160400(n),n=1..120) ; # R. J. Mathar, May 26 2009

Mathematica

a[n_] := SelectFirst[Range[n], GCD @@ FactorInteger[n*#][[;; , 2]] > 1 &]; a[1] = 1; Array[a, 100] (* Amiram Eldar, Jul 09 2022 *)

Formula

a(n) = A087320(n)/n.

a(n) = A007913(n) for n cubefree, a(n) = 1 for n in A001597. - Charlie Neder, Dec 26 2018

Extensions

More terms from R. J. Mathar, May 26 2009