A192268 Anti-abundant numbers.

7, 10, 11, 12, 13, 14, 15, 17, 18, 20, 21, 22, 23, 25, 27, 28, 30, 31, 32, 33, 35, 37, 38, 39, 40, 42, 43, 45, 46, 47, 48, 49, 50, 52, 53, 55, 57, 58, 59, 60, 62, 63, 65, 66, 67, 68, 70, 71, 72, 73, 74, 75, 76, 77, 78, 80, 81, 82, 83, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 97, 98, 99, 100, 101, 102, 103, 104, 105, 107, 108, 109, 110, 111, 112, 113

Offset

1,1

Comments

An anti-abundant number is a number n for which sigma*(n) > n, where sigma*(n) is the sum of the anti-divisors of n. Like A005101 but using anti-divisors.

Links

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

Formula

A000027 = A073930 UNION A192267 UNION {this set}.

Example

25 is anti-abundant because its anti-divisors are 2, 3, 7, 10, 17 and their sum is 39 > 25.

Maple

isA192268 := proc(n) A066417(n) > n ; end proc:
for n from 1 to 500 do if isA192268(n) then printf("%d, ", n); end if; end do: # R. J. Mathar, Jul 04 2011

Mathematica

antiAbQ[n_] := Total[Cases[Range[2, n - 1], _?(Abs[Mod[n, #] - #/2] < 1 &)]] > n; Select[Range[120], antiAbQ] (* Amiram Eldar, Jan 13 2022 after Michael De Vlieger at A066417 *)

Prog

(Python)
from itertools import count, islice
from sympy import divisor_sigma, multiplicity
def A192268gen(): return filter(lambda n:divisor_sigma(2*n-1)+divisor_sigma(2*n+1)+divisor_sigma(n//2**(k:=multiplicity(2, n)))*2**(k+1)-7*n-2 > 0, count(2))
A192268_list = list(islice(A192268gen(), 16)) # Chai Wah Wu, Dec 23 2021

Crossrefs

Cf. A066417, A005101, A066272, A192267.

Sequence in context: A317336 A079004 A265311 * A117319 A120645 A168158

Adjacent sequences: A192265 A192266 A192267 * A192269 A192270 A192271

Keyword

nonn,easy

Author

Paolo P. Lava, Jun 28 2011

Status

approved