A229090 Numbers n such that sigma(n) mod n > antisigma(n) mod n, where sigma(n) = A000203(n) = sum of divisors of n, antisigma(n) = A024816(n) = sum of non-divisors of n.

2, 8, 10, 12, 15, 16, 21, 24, 30, 32, 42, 44, 45, 50, 52, 60, 63, 64, 68, 75, 76, 80, 92, 99, 105, 110, 116, 117, 124, 126, 128, 130, 135, 136, 140, 144, 147, 148, 150, 152, 153, 154, 160, 164, 165, 168, 170, 171, 172, 182, 184, 188, 189, 190, 195, 198, 200

Offset

1,1

Comments

Numbers n such that A229087(n) = A000203(n) mod n - A024816(n) mod n = A054024(n) - A229110(n) > 0.

Complement of union A229088 and A229089 with respect to A000027, where A229088 = numbers n such that sigma(n) mod n = antisigma(n) mod n, A229089 = numbers n such that sigma(n) mod n < antisigma(n) mod n.

Links

Jaroslav Krizek, Table of n, a(n) for n = 1..10000

Example

Number 12 is in sequence because sigma(12) mod 12 = 28 mod 12 = 4 > antisigma(12) mod 12 = 50 mod 12 = 2.

Mathematica

smQ[n_]:=Module[{sig=DivisorSigma[1, n]}, Mod[sig, n]>Mod[(n(n+1))/2-sig, n]]; Select[Range[200], smQ] (* Harvey P. Dale, Dec 23 2013 *)

Crossrefs

Cf. A000203 (sigma(n)), A024816 (antisigma(n)).

Cf. A054024 (sigma(n) mod n), A229110 (antisigma(n) mod n).

Sequence in context: A084124 A081693 A022298 * A265670 A297999 A287088

Adjacent sequences: A229087 A229088 A229089 * A229091 A229092 A229093

Keyword

nonn

Author

Jaroslav Krizek, Oct 24 2013

Status

approved