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A083244 n is in the sequence iff number of numbers unrelated to n is larger than that of related ones[=divisors and coprimes] to n: A045763(n)>A073757(n) or A045763(n)>n/2 or A073757(n)<n/2. 4
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

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

FORMULA

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

EXAMPLE

n = 42 is here 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

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Last modified May 6 09:45 EDT 2021. Contains 343580 sequences. (Running on oeis4.)