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%I #26 Sep 17 2023 13:57:38
%S 72,216,76326,101526,116646,146886,298086,369366,624966,1375926,
%T 1532166,1558086,1598406,1750326,1789206,1866246,1991526,2516406,
%U 2540886,2620806,2681286,2827446,3151446,3196806,3236406,3489126
%N Arithmetic progressions of at least 4 terms with common difference 6 having the same value of phi(x) start at these numbers.
%C From _Wolfdieter Lang_, Jan 11 2021: (Start)
%C Conjecture: a(n) == 0 (mod 6) for n >= 1. After division by 6 the sequence becomes [12, 36, 12721, 16921, 19441, 24481, 49681, 61561, 104161, 229321, 255361, 259681, 266401, 291721, 298201, 311041, 331921, ...].
%C 6*A163573 is a subsequence. See A163573 for the proof. Note that not all a(n), for n >= 3, are obtained by 6*A163573. The first such term is a(115) = 31850496, and a(115)/6 = 5308416 which is not a prime number, hence not a term of A163573. (End)
%H Jud McCranie, <a href="/A050498/b050498.txt">Table of n, a(n) for n = 1..10000</a>
%e phi(72) = phi(78) = phi(84) = phi(90) = 24, so 72 is in the sequence.
%o (PARI) isok(k) = #Set(vector(4, i, eulerphi(k+(i-1)*6))) == 1; \\ _Michel Marcus_, Sep 17 2023
%Y Cf. A000010, A039670, A163573.
%K nonn
%O 1,1
%A _Jud McCranie_, Dec 27 1999
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