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

1,2

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 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.

Links

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

Example

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.

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);

Crossrefs

Cf. A004394, A066417, A192268.

Sequence in context: A190213 A216574 A216561 * A284618 A101759 A089560

Adjacent sequences: A192266 A192267 A192268 * A192270 A192271 A192272

Keyword

nonn

Author

Paolo P. Lava, Jun 28 2011

Extensions

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

Status

approved