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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.
4

%I #23 Sep 03 2021 01:55:03

%S 42,54,60,66,70,72,78,84,90,96,98,100,102,108,110,114,120,126,130,132,

%T 138,140,144,150,154,156,160,162,168,170,174,180,182,186,190,192,196,

%U 198,200,204,210,216,220,222,224,228,230,234,238,240,242,246,250,252

%N 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.

%H Robert Israel, <a href="/A083244/b083244.txt">Table of n, a(n) for n = 1..10000</a>

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

%e 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.

%p filter:= n -> n > 2*(numtheory:-tau(n) + numtheory:-phi(n)-1):

%p select(filter, [$1..1000]); # _Robert Israel_, May 15 2017

%t 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}]

%t (* Second program: *)

%t Select[Range@ 256, # - (DivisorSigma[0, #] + EulerPhi[#] - 1) > #/2 &] (* _Michael De Vlieger_, Jul 22 2017 *)

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

%K nonn

%O 1,1

%A _Labos Elemer_, May 07 2003