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A354189 Numbers k for which phi(A267099(k)) is equal to phi(k), where A267099 is fully multiplicative involution swapping the positions of 4k+1 and 4k+3 primes, and phi is Euler totient function.

%I A354189 #14 May 28 2022 16:37:30
%S A354189 1,2,4,8,15,16,30,32,35,39,60,64,70,78,91,120,128,140,156,182,187,225,
%T A354189 240,256,280,312,364,374,450,480,512,551,560,624,728,748,851,900,960,
%U A354189 1024,1102,1120,1248,1271,1365,1456,1496,1702,1800,1920,2048,2204,2240,2279,2496,2542,2730,2747,2759,2805,2867,2912,2992
%N A354189 Numbers k for which phi(A267099(k)) is equal to phi(k), where A267099 is fully multiplicative involution swapping the positions of 4k+1 and 4k+3 primes, and phi is Euler totient function.
%C A354189 Not a subsequence of A072202. The first term that is included here, but not in that sequence is 69037, as A000010(69037) = A354102(69037) = 62400, although 69037 = 17*31*131. See A354194.
%H A354189 Antti Karttunen, <a href="/A354189/b354189.txt">Table of n, a(n) for n = 1..5200</a>
%F A354189 {k | A354102(k) == A000010(k)}.
%o A354189 (PARI)
%o A354189 A354188(n) = (eulerphi(A267099(n)) == eulerphi(n)); \\ Uses the program given in A267099.
%o A354189 isA354189(n) = A354188(n);
%Y A354189 Positions of zeros in A354101.
%Y A354189 Subsequence of A354109.
%Y A354189 Cf. A000079, A354192, A354194 (subsequences), A354188 (characteristic function).
%Y A354189 Cf. A000010, A072202, A267099, A354102, A354106.
%K A354189 nonn
%O A354189 1,2
%A A354189 _Antti Karttunen_, May 19 2022