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Numbers k such that phi(k*(k+1)*(k+2)/3)/phi(k) is not an integer where phi(k) is the Euler totient function A000010(k).
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%I #13 Mar 01 2020 04:45:19

%S 9,45,81,99,135,225,234,261,288,351,423,450,459,477,504,567,585,639,

%T 666,819,837,855,900,927,954,981,1017,1134,1179,1242,1305,1359,1431,

%U 1449,1485,1521,1593,1638,1710,1773,1908,1953,1971,2025,2061,2097,2151

%N Numbers k such that phi(k*(k+1)*(k+2)/3)/phi(k) is not an integer where phi(k) is the Euler totient function A000010(k).

%C For every n, a(n)==0 (mod 3).

%H Amiram Eldar, <a href="/A067536/b067536.txt">Table of n, a(n) for n = 1..10000</a>

%t Select[Range[2000], ! Divisible[EulerPhi[#*(# + 1)*(# + 2)/3], EulerPhi[#]] &] (* _Amiram Eldar_, Mar 01 2020 *)

%o (PARI) is(n)=eulerphi(n*(n+1)*(n+2)/3)%eulerphi(n) \\ _Charles R Greathouse IV_, Mar 05 2013

%Y Cf. A000010, A007290.

%K nonn

%O 1,1

%A _Benoit Cloitre_, Jan 28 2002