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

Author

Antti Karttunen, May 18 2022

Keywords

• nonn
• mult

Links

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

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.

Programs

PARI

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

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).