login
Smallest nonsquarefree multiple of n.
1

%I #21 Jul 02 2023 02:18:15

%S 4,4,9,4,20,12,28,8,9,20,44,12,52,28,45,16,68,18,76,20,63,44,92,24,25,

%T 52,27,28,116,60,124,32,99,68,140,36,148,76,117,40,164,84,172,44,45,

%U 92,188,48,49,50,153,52,212,54,220,56,171,116,236,60,244,124,63,64,260,132

%N Smallest nonsquarefree multiple of n.

%H Harvey P. Dale, <a href="/A088613/b088613.txt">Table of n, a(n) for n = 1..1000</a>

%F If n is nonsquarefree, then a(n) = n. If n is an even squarefree integer, then a(n) = 2*n. If n is an odd squarefree multiple of 3, then a(n) = 3*n. If n is a squarefree integer not divisible by either 2 or 3, then a(n) = 4*n. a(p) = 4p if p is a prime >= 5. - _Leroy Quet_, May 14 2008

%F Sum_{k=1..n} a(k) ~ c * n^2, where c = 1/2 + 13/(2*Pi^2) = 1.158587... . - _Amiram Eldar_, Jul 02 2023

%t snmn[n_]:=Which[!SquareFreeQ[n],n,EvenQ[n],2n,Mod[n,3]==0,3n,True,4n]; Array[snmn,70] (* _Harvey P. Dale_, Nov 11 2020 *)

%Y Cf. A013929.

%K easy,nonn

%O 1,1

%A _Amarnath Murthy_, Oct 16 2003

%E More terms from _Ray Chandler_, Oct 18 2003