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

1,2

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

Formula

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

Prog

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

Crossrefs

Positions of zeros in A354101.

Subsequence of A354109.

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

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

Sequence in context: A277166 A078613 A072202 * A275474 A354192 A076351

Adjacent sequences: A354186 A354187 A354188 * A354190 A354191 A354192

Keyword

nonn

Author

Antti Karttunen, May 19 2022

Status

approved