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%I #21 Jan 13 2022 04:24:22
%S 1,2,3,4,6,9,16,19,24,26,29,34,36,44,51,54,61,64,69,79,89,96,106,114,
%T 131,134,139,141,146,156,159,166,169,174,191,194,201,209,211,216,219,
%U 224,226,236,239,244,246,251,254,261,271,274,289,296,299,309,316
%N Anti-deficient numbers.
%C An anti-deficient number is a number n for which sigma*(n) < n, where sigma*(n) is the sum of the anti-divisors of n. Like A005100 but using anti-divisors. There are only 22 anti-deficient numbers less than 100, 159 less than 1000 and 1547 less than 10000. From an empirical observation it seems that the anti-deficient are approximately less than 18% of the anti-abundant.
%H Amiram Eldar, <a href="/A192267/b192267.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..5000 from Paolo P. Lava)
%F A000027 = A073930 UNION {this set} UNION A192268.
%e 24 is anti-deficient because its anti-divisors are 7, 16 and their sum is 23 < 24.
%p isA192267 := proc(n) A066417(n) < n ; end proc:
%p for n from 1 to 500 do if isA192267(n) then printf("%d,",n); end if; end do: # _R. J. Mathar_, Jul 04 2011
%t antiDefQ[n_] := Total[Cases[Range[2, n - 1], _?(Abs[Mod[n, #] - #/2] < 1 &)]] < n; Select[Range[300], antiDefQ] (* _Amiram Eldar_, Jan 13 2022 after _Michael De Vlieger_ at A066417 *)
%Y Cf. A066417, A005100, A066272, A192268.
%K nonn,easy
%O 1,2
%A _Paolo P. Lava_, Jun 28 2011
%E Edited by _Ray Chandler_, Dec 05 2011
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