A354189 - OEIS

%I #14 May 28 2022 16:37:30

%S 1,2,4,8,15,16,30,32,35,39,60,64,70,78,91,120,128,140,156,182,187,225,

%T 240,256,280,312,364,374,450,480,512,551,560,624,728,748,851,900,960,

%U 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 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 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 Antti Karttunen, <a href="/A354189/b354189.txt">Table of n, a(n) for n = 1..5200</a>

%F {k | A354102(k) == A000010(k)}.

%o (PARI)

%o A354188(n) = (eulerphi(A267099(n)) == eulerphi(n)); \\ Uses the program given in A267099.

%o isA354189(n) = A354188(n);

%Y Positions of zeros in A354101.

%Y Subsequence of A354109.

%Y Cf. A000079, A354192, A354194 (subsequences), A354188 (characteristic function).

%Y Cf. A000010, A072202, A267099, A354102, A354106.

%K nonn

%O 1,2

%A _Antti Karttunen_, May 19 2022