A354102 a(n) = phi(A267099(n)), where A267099 is fully multiplicative involution swapping the positions of 4k+1 and 4k+3 primes, and phi is Euler totient function.

1, 1, 4, 2, 2, 4, 12, 4, 20, 2, 16, 8, 6, 12, 8, 8, 10, 20, 28, 4, 48, 16, 36, 16, 6, 6, 100, 24, 18, 8, 40, 16, 64, 10, 24, 40, 22, 28, 24, 8, 30, 48, 52, 32, 40, 36, 60, 32, 156, 6, 40, 12, 42, 100, 32, 48, 112, 18, 72, 16, 46, 40, 240, 32, 12, 64, 88, 20, 144, 24, 96, 80, 58, 22, 24, 56, 192, 24, 100, 16, 500

Offset

1,3

Links

Antti Karttunen, Table of n, a(n) for n = 1..19683

Formula

Multiplicative with a(p^e) = (q-1) * q^(e-1), where q = A267101(A000720(p)).

a(n) = A000010(A267099(n)).

a(n) = Sum_{d|n} A008683(n/d) * A267099(d).

a(n) = A354101(n) + A000010(n) = A354190(n) - A354191(n).

For all n >= 0, a(4n+2) = a(2n+1).

Prog

(PARI) A354102(n) = eulerphi(A267099(n)); \\ Uses the program given in A267099.

Crossrefs

Möbius transform of A267099.

Cf. A000720, A008683, A267101, A354101, A354103, A354104 (Dirichlet inverse), A354105 (sum with it), A354106, A354107 (a(n) mod 4), A354190, A354191.

Coincides with A000010 on A354189.

Sequence in context: A289762 A360855 A064213 * A245518 A217462 A016510

Adjacent sequences: A354099 A354100 A354101 * A354103 A354104 A354105

Keyword

nonn,mult

Author

Antti Karttunen, May 18 2022

Status

approved