

A192267


Antideficient numbers.


5



1, 2, 3, 4, 6, 9, 16, 19, 24, 26, 29, 34, 36, 44, 51, 54, 61, 64, 69, 79, 89, 96, 106, 114, 131, 134, 139, 141, 146, 156, 159, 166, 169, 174, 191, 194, 201, 209, 211, 216, 219, 224, 226, 236, 239, 244, 246, 251, 254, 261, 271, 274, 289, 296, 299, 309, 316
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OFFSET

1,2


COMMENTS

An antideficient number is a number n for which sigma*(n) < n, where sigma*(n) is the sum of the antidivisors of n. Like A005100 but using antidivisors. There are only 22 antideficient numbers less than 100, 159 less than 1000 and 1547 less than 10000. From an empirical observation it seems that the antideficient are approximately less than 18% of the antiabundant.


LINKS

Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..5000 from Paolo P. Lava)


FORMULA

A000027 = A073930 UNION {this set} UNION A192268.


EXAMPLE

24 is antideficient because its antidivisors are 7, 16 and their sum is 23 < 24.


MAPLE

isA192267 := proc(n) A066417(n) < n ; end proc:
for n from 1 to 500 do if isA192267(n) then printf("%d, ", n); end if; end do: # R. J. Mathar, Jul 04 2011


MATHEMATICA

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 *)


CROSSREFS

Cf. A066417, A005100, A066272, A192268.
Sequence in context: A268710 A223900 A326020 * A331022 A256774 A213682
Adjacent sequences: A192264 A192265 A192266 * A192268 A192269 A192270


KEYWORD

nonn,easy


AUTHOR

Paolo P. Lava, Jun 28 2011


EXTENSIONS

Edited by Ray Chandler, Dec 05 2011


STATUS

approved



