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A192267 Anti-deficient 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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified December 7 13:02 EST 2022. Contains 358656 sequences. (Running on oeis4.)