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.

1, 2, 4, 8, 15, 16, 30, 32, 35, 39, 60, 64, 70, 78, 91, 120, 128, 140, 156, 182, 187, 225, 240, 256, 280, 312, 364, 374, 450, 480, 512, 551, 560, 624, 728, 748, 851, 900, 960, 1024, 1102, 1120, 1248, 1271, 1365, 1456, 1496, 1702, 1800, 1920, 2048, 2204, 2240, 2279, 2496, 2542, 2730, 2747, 2759, 2805, 2867, 2912, 2992

Offset: 1

Author

Antti Karttunen, May 19 2022

Keywords

• nonn

Comments

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.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..5200

Crossrefs

Positions of zeros in A354101.

Subsequence of A354109.

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

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

Programs

PARI

A354188(n) = (eulerphi(A267099(n)) == eulerphi(n)); \\ Uses the program given in A267099.
isA354189(n) = A354188(n);

Formula

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