A192269 - OEIS

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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

(list; graph; refs; listen; history; text; internal format)

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;