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

%I A100994 #36 Dec 31 2021 11:41:34
%S A100994 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,
%T A100994 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,
%U A100994 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
%N A100994 If n is a prime power p^m, m >= 1, then n, otherwise 1.
%C A100994 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
%H A100994 G. C. Greubel, <a href="/A100994/b100994.txt">Table of n, a(n) for n = 1..1000</a>
%F A100994 a(n) = A014963(n)^A100995(n) = n^A010055(n);
%F A100994 a(A000961(n)) = A000961(n).
%F A100994 a(n) = 1 + (n-1)*floor(1/A001221(n)) for n > 1. - _Enrique Pérez Herrero_, Sep 24 2011
%t A100994 A100994[1]:=1; A100994[n_] := (n-1)*(Floor[1/PrimeNu[n]])+1; Array[A100994,100] (* _Enrique Pérez Herrero_, Sep 24 2011 *)
%t A100994 a[n_] := If[PrimePowerQ[n], n, 1];
%t A100994 Array[a, 100] (* _Jean-François Alcover_, Mar 26 2020 *)
%o A100994 (PARI) a(n) = if (isprimepower(n), n, 1); \\ _Michel Marcus_, Mar 18 2018
%Y A100994 Cf. A000961, A001221, A010055, A014963, A100995.
%K A100994 nonn
%O A100994 1,2
%A A100994 _Reinhard Zumkeller_, Nov 26 2004
%E A100994 Definition edited to remove ambiguity by _Daniel Forgues_, Aug 18 2009