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%I #23 Jan 13 2022 04:24:42
%S 7,10,11,12,13,14,15,17,18,20,21,22,23,25,27,28,30,31,32,33,35,37,38,
%T 39,40,42,43,45,46,47,48,49,50,52,53,55,57,58,59,60,62,63,65,66,67,68,
%U 70,71,72,73,74,75,76,77,78,80,81,82,83,84,85,86,87,88,90,91,92,93,94,95,97,98,99,100,101,102,103,104,105,107,108,109,110,111,112,113
%N Anti-abundant numbers.
%C An anti-abundant number is a number n for which sigma*(n) > n, where sigma*(n) is the sum of the anti-divisors of n. Like A005101 but using anti-divisors.
%H Amiram Eldar, <a href="/A192268/b192268.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..5000 from Paolo P. Lava)
%F A000027 = A073930 UNION A192267 UNION {this set}.
%e 25 is anti-abundant because its anti-divisors are 2, 3, 7, 10, 17 and their sum is 39 > 25.
%p isA192268 := proc(n) A066417(n) > n ; end proc:
%p for n from 1 to 500 do if isA192268(n) then printf("%d,",n); end if; end do: # _R. J. Mathar_, Jul 04 2011
%t antiAbQ[n_] := Total[Cases[Range[2, n - 1], _?(Abs[Mod[n, #] - #/2] < 1 &)]] > n; Select[Range[120], antiAbQ] (* _Amiram Eldar_, Jan 13 2022 after _Michael De Vlieger_ at A066417 *)
%o (Python)
%o from itertools import count, islice
%o from sympy import divisor_sigma, multiplicity
%o def A192268gen(): return filter(lambda n:divisor_sigma(2*n-1)+divisor_sigma(2*n+1)+divisor_sigma(n//2**(k:=multiplicity(2,n)))*2**(k+1)-7*n-2 > 0,count(2))
%o A192268_list = list(islice(A192268gen(),16)) # _Chai Wah Wu_, Dec 23 2021
%Y Cf. A066417, A005101, A066272, A192267.
%K nonn,easy
%O 1,1
%A _Paolo P. Lava_, Jun 28 2011
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