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A192269
Super anti-abundant numbers.
2
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
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
KEYWORD
nonn
AUTHOR
Paolo P. Lava, Jun 28 2011
EXTENSIONS
a(26)-a(42) from Donovan Johnson, Sep 07 2011
STATUS
approved