A254572 - OEIS

%I #24 Feb 09 2023 04:42:41

%S 6,6,6,12,20,6,28,24,18,20,66,12,78,28,30,48,102,18,114,20,42,66,138,

%T 24,100,78,54,28,174,30,186,96,66,102,70,36,222,114,78,40,246,42,258,

%U 88,90,138,282,48,196,100,102,104,318,54,220,56,114,174,354,60

%N Least multiple of n that is abundant or perfect (A023196).

%C See A254571(n) = a(n)/n for the multipliers.

%C Very often a(n) = A064162(n), but the definition of the latter requires strict abundance.

%H Robert Israel, <a href="/A254572/b254572.txt">Table of n, a(n) for n = 1..10000</a>

%p f:= proc(n) local k; uses numtheory;

%p       for k from 1 to 4 do if sigma(k*n)>=2*k*n then return k*n fi od:

%p       6*n

%p end proc:

%p map(f, [$1..100]); # _Robert Israel_, Feb 10 2019

%t a[n_] := Do[If[DivisorSigma[1, k*n] >= 2*k*n, Return[k*n]], {k, {1, 2, 3, 4, 6}}];

%t Table[a[n], {n, 1, 100}] (* _Jean-François Alcover_, Feb 09 2023 *)

%o (PARI) a(n) = forstep(m=n,6*n,n,if(sigma(m)>=2*m,return(m)))

%Y Cf. A023196, A064162, A254571.

%K nonn

%O 1,1

%A _Jeppe Stig Nielsen_, Feb 01 2015