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%I #10 Jul 17 2022 02:21:56
%S 8,9,18,27,44,45,53,62,80,81,90,98,99,108,116,126,134,135,143,162,171,
%T 189,198,224,225,233,234,251,260,261,270,279,287,288,296,315,332,350,
%U 351,387,413,422,423,441,449,450,458,459,468,476,477,503,504,512,522
%N Numbers k such that phi(k*(k+1)*(k+2)/6)/phi(k*(k+1)/2) is not an integer where phi(k) = A000010(k) is the Euler totient function.
%C Often a(k) == 0 (mod 3) and if a(k+1) - a(k) = 1 then a(k+1) == 0 (mod 3).
%H Amiram Eldar, <a href="/A067544/b067544.txt">Table of n, a(n) for n = 1..10000</a>
%t Select[Range[500], ! Divisible[EulerPhi[#*(# + 1)*(# + 2)/6], EulerPhi[#*(# + 1)/2]] &] (* _Amiram Eldar_, Jul 17 2022 *)
%Y Cf. A000010, A000217, A000292, A086700.
%K nonn
%O 1,1
%A _Benoit Cloitre_, Jan 28 2002
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