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Numbers k such that phi(k*(k+1)*(k+2)*(k+3)/4!)/phi(k*(k+1)*(k+2)/3!) is not an integer where phi(n) = A000010(n) is the Euler totient function.
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%I #15 Dec 19 2023 16:49:39

%S 6,8,16,24,40,46,54,56,64,78,80,104,118,126,128,136,144,160,176,198,

%T 208,224,240,248,280,304,328,344,358,360,376,414,416,440,464,486,488,

%U 496,520,526,544,560,568,584,616,630,640,656,680,688,726,736,784

%N Numbers k such that phi(k*(k+1)*(k+2)*(k+3)/4!)/phi(k*(k+1)*(k+2)/3!) is not an integer where phi(n) = A000010(n) is the Euler totient function.

%o (PARI) isok(k) = denominator(eulerphi(k*(k+1)*(k+2)*(k+3)/4!)/eulerphi(k*(k+1)*(k+2)/3!)) != 1; \\ _Michel Marcus_, Dec 19 2023

%Y Cf. A000010 (phi).

%K nonn

%O 1,1

%A _Benoit Cloitre_, Jan 28 2002

%E Incorrect 203 removed by _Sean A. Irvine_, Dec 19 2023