A100994 If n is a prime power p^m, m >= 1, then n, otherwise 1.

1, 2, 3, 4, 5, 1, 7, 8, 9, 1, 11, 1, 13, 1, 1, 16, 17, 1, 19, 1, 1, 1, 23, 1, 25, 1, 27, 1, 29, 1, 31, 32, 1, 1, 1, 1, 37, 1, 1, 1, 41, 1, 43, 1, 1, 1, 47, 1, 49, 1, 1, 1, 53, 1, 1, 1, 1, 1, 59, 1, 61, 1, 1, 64, 1, 1, 67, 1, 1, 1, 71, 1, 73, 1, 1, 1, 1, 1, 79, 1, 81, 1, 83, 1, 1, 1, 1, 1, 89, 1, 1

Offset: 1

Author

Reinhard Zumkeller, Nov 26 2004

Keywords

• nonn

Comments

a(n) is the smallest positive integer such that n divides lcm(a(1), a(2), a(3), ..., a(n)), for all positive integers n. - Leroy Quet, May 01 2007

Links

• G. C. Greubel, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000961, A001221, A010055, A014963, A100995.

Programs

Mathematica

A100994[1]:=1; A100994[n_] := (n-1)*(Floor[1/PrimeNu[n]])+1; Array[A100994,100] (* Enrique Pérez Herrero, Sep 24 2011 *)
a[n_] := If[PrimePowerQ[n], n, 1];
Array[a, 100] (* Jean-François Alcover, Mar 26 2020 *)

PARI

a(n) = if (isprimepower(n), n, 1); \\ Michel Marcus, Mar 18 2018

Formula

a(n) = A014963(n)^A100995(n) = n^A010055(n);

a(A000961(n)) = A000961(n).

a(n) = 1 + (n-1)*floor(1/A001221(n)) for n > 1. - Enrique Pérez Herrero, Sep 24 2011

Extensions

Definition edited to remove ambiguity by Daniel Forgues, Aug 18 2009