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

Author

Paolo P. Lava, Jun 28 2011

Keywords

• nonn
• easy

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.

Examples

			24 is anti-deficient because its anti-divisors are 7, 16 and their sum is 23 < 24.
		

Links

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

Crossrefs

Cf. A066417, A005100, A066272, A192268.

Programs

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 *)

Formula

A000027 = A073930 UNION {this set} UNION A192268.

Extensions

Edited by Ray Chandler, Dec 05 2011