A073482 Largest prime factor of the n-th squarefree number.

1, 2, 3, 5, 3, 7, 5, 11, 13, 7, 5, 17, 19, 7, 11, 23, 13, 29, 5, 31, 11, 17, 7, 37, 19, 13, 41, 7, 43, 23, 47, 17, 53, 11, 19, 29, 59, 61, 31, 13, 11, 67, 23, 7, 71, 73, 37, 11, 13, 79, 41, 83, 17, 43, 29, 89, 13, 31, 47, 19, 97, 101, 17, 103, 7, 53, 107, 109, 11, 37, 113, 19, 23, 59, 17, 61, 41

Offset

1,2

Links

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

Jean-Marie De Koninck and Rafael Jakimczuk, Summing the largest prime factor over integer sequences, Revista de la Unión Matemática Argentina, Vol. 67, No. 1 (2024), pp. 27-35.

Formula

a(n) = A006530(A005117(n)).

a(n) = A265668(n, A001221(n)). - Reinhard Zumkeller, Dec 13 2015

Sum_{A005117(n) <= x} a(n) = Sum_{i=1..k} d_i * x^2/log(x)^i + O(x^2/log(x)^(k+1)), for any given positive integer k, where d_i are constants, d_1 = 15/(2*Pi^2) = 0.759908... (A323669) (De Koninck and Jakimczuk, 2024). - Amiram Eldar, Mar 03 2024

Maple

issquarefree := proc(n::integer) local nf, ifa, lar; nf := op(2, ifactors(n)); for ifa from 1 to nops(nf) do lar := op(1, op(ifa, nf)); if op(2, op(ifa, nf)) >= 2 then RETURN(0); fi; od : RETURN(lar); end: printf("1, "); for n from 2 to 100 do lfa := issquarefree(n); if lfa > 0 then printf("%a, ", lfa); fi; od : # R. J. Mathar, Apr 02 2006

Mathematica

FactorInteger[#][[-1, 1]]& /@ Select[Range[100], SquareFreeQ] (* Jean-François Alcover, Feb 01 2018 *)
s[n_] := Module[{f = FactorInteger[n]}, If[AllTrue[f[[;; , 2]], # < 2 &], f[[-1, 1]], Nothing]]; Array[s, 200] (* Amiram Eldar, Mar 03 2024 *)

Prog

(Haskell)
a073482 = a006530 . a005117  -- Reinhard Zumkeller, Feb 04 2012
(PARI) do(x)=my(v=List([1])); forfactored(n=2, x\1, if(vecmax(n[2][, 2])==1, listput(v, vecmax(n[2][, 1])))); Vec(v) \\ Charles R Greathouse IV, Nov 05 2017

Crossrefs

Cf. A073481, A001221, A005117, A006530, A265668, A323669.

Sequence in context: A117369 A117366 A341643 * A318411 A225680 A346091

Adjacent sequences: A073479 A073480 A073481 * A073483 A073484 A073485

Keyword

nonn,easy

Author

Reinhard Zumkeller, Aug 03 2002

Extensions

More terms from Jason Earls, Aug 06 2002

Status

approved