A192269 Super anti-abundant numbers.

1, 3, 4, 5, 7, 13, 17, 32, 38, 45, 67, 77, 143, 203, 247, 473, 682, 787, 1463, 2678, 2992, 3465, 8662, 10868, 16065, 25987, 26163, 29452, 112613, 157658, 202702, 233415, 363825, 795217, 1148647, 1914412, 2139637, 5743237, 5743238, 8393963, 11869357, 64353712

Offset: 1

Author

Paolo P. Lava, Jun 28 2011

Keywords

• nonn

Comments

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 kA066417(n)/n.

Examples

			1 -> sigma*(1)/1 = 0/1 = 0;
3 -> sigma*(3)/3 = 2/3 = 0.6666...;
4 -> sigma*(4)/4 = 3/4 = 0.75;
5 -> sigma*(5)/5 = 5/5 = 1;
7 -> sigma*(7)/7 = 10/7 = 1.4285...; etc.
		

Links

• Jud McCranie, Table of n, a(n) for n = 1..66

Crossrefs

Cf. A004394, A066417, A192268.

Programs

Maple

with(numtheory); P:= proc(n) local a,k,i,j,s; s:=0; print(1);
for i from 3 to n do
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;
if a/i>s then s:=a/i; print(i); fi; od; end: P(50000);

Extensions

a(26)-a(42) from Donovan Johnson, Sep 07 2011