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

1,2

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

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

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 *)

Prog

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

Crossrefs

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

Sequence in context: A332425 A286594 A241479 * A140523 A237517 A332883

Adjacent sequences: A100991 A100992 A100993 * A100995 A100996 A100997

Keyword

nonn

Author

Reinhard Zumkeller, Nov 26 2004

Extensions

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

Status

approved