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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.
15
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
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
KEYWORD
nonn,mult
AUTHOR
Antti Karttunen, May 18 2022
STATUS
approved