A192267 Anti-deficient numbers.

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

Offset

1,2

Comments

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.

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 anti-deficient because its anti-divisors 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