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A192269 Super anti-abundant numbers. 1
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

Table of n, a(n) for n=1..42.

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

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Last modified April 19 18:37 EDT 2019. Contains 322290 sequences. (Running on oeis4.)