A083244 k is in the sequence iff the number of numbers unrelated to k is larger than that of related ones[=divisors and coprimes] to k: A045763(k) > A073757(k) or A045763(k) > k/2 or A073757(k) < k/2.

42, 54, 60, 66, 70, 72, 78, 84, 90, 96, 98, 100, 102, 108, 110, 114, 120, 126, 130, 132, 138, 140, 144, 150, 154, 156, 160, 162, 168, 170, 174, 180, 182, 186, 190, 192, 196, 198, 200, 204, 210, 216, 220, 222, 224, 228, 230, 234, 238, 240, 242, 246, 250, 252

Offset

1,1

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Formula

Numbers k such that k - d(k) - phi(k) + 1 > k/2.

Example

k = 42 is a term because d = 8 divisors, r = 12 coprimes and u = 23 unrelated belong to it: u = 23 > 19 = 8 + 12 - 1 = d + r - 1.

Maple

filter:= n -> n > 2*(numtheory:-tau(n) + numtheory:-phi(n)-1):
select(filter, [$1..1000]); # Robert Israel, May 15 2017

Mathematica

Do[r=EulerPhi[n]; d=DivisorSigma[0, n]; u=n-d-r+1; If[Greater[u, n/2], Print[n, {d, r, u}]], {n, 1, 100}]
(* Second program: *)
Select[Range@ 256, # - (DivisorSigma[0, #] + EulerPhi[#] - 1) > #/2 &] (* Michael De Vlieger, Jul 22 2017 *)

Crossrefs

Cf. A000005, A000010, A045763, A073757, A020488, A083243, A083245.

Sequence in context: A175103 A116262 A156394 * A125009 A008886 A341129

Adjacent sequences: A083241 A083242 A083243 * A083245 A083246 A083247

Keyword

nonn

Author

Labos Elemer, May 07 2003

Status

approved