cp's OEIS Frontend

A192269 Super anti-abundant numbers.

%I A192269 #26 Oct 23 2019 02:48:14
%S A192269 1,3,4,5,7,13,17,32,38,45,67,77,143,203,247,473,682,787,1463,2678,
%T A192269 2992,3465,8662,10868,16065,25987,26163,29452,112613,157658,202702,
%U A192269 233415,363825,795217,1148647,1914412,2139637,5743237,5743238,8393963,11869357,64353712
%N A192269 Super anti-abundant numbers.
%C A192269 Like A004394 but using anti-divisors. A super anti-abundant number is a number n such that sigma*(n)/n > sigma*(k)/k for all k<n, where sigma*(n) is the sum of the anti-divisors of n. This is the RECORDS transform of the sequence of fractions A066417(n)/n.
%H A192269 Jud McCranie, <a href="/A192269/b192269.txt">Table of n, a(n) for n = 1..66</a>
%e A192269 1 -> sigma*(1)/1 = 0/1 = 0;
%e A192269 3 -> sigma*(3)/3 = 2/3 = 0.6666...;
%e A192269 4 -> sigma*(4)/4 = 3/4 = 0.75;
%e A192269 5 -> sigma*(5)/5 = 5/5 = 1;
%e A192269 7 -> sigma*(7)/7 = 10/7 = 1.4285...; etc.
%p A192269 with(numtheory); P:= proc(n) local a,k,i,j,s; s:=0; print(1);
%p A192269 for i from 3 to n do
%p A192269 k:=0; j:=i; while j mod 2 <> 1 do k:=k+1; j:=j/2; od; a:=sigma(2*i+1)+sigma(2*i-1)+sigma(i/2^k)*2^(k+1)-6*i-2;
%p A192269 if a/i>s then s:=a/i; print(i); fi; od; end: P(50000);
%Y A192269 Cf. A004394, A066417, A192268.
%K A192269 nonn
%O A192269 1,2
%A A192269 _Paolo P. Lava_, Jun 28 2011
%E A192269 a(26)-a(42) from _Donovan Johnson_, Sep 07 2011