A354094 a(n) = phi(A354091(n)), where A354091 is fully multiplicative prime shift which replaces the primes of the form 3k+2 by the next larger such prime, while other primes stay as they are, and phi is Euler totient function.

1, 4, 2, 20, 10, 8, 6, 100, 6, 40, 16, 40, 12, 24, 20, 500, 22, 24, 18, 200, 12, 64, 28, 200, 110, 48, 18, 120, 40, 80, 30, 2500, 32, 88, 60, 120, 36, 72, 24, 1000, 46, 48, 42, 320, 60, 112, 52, 1000, 42, 440, 44, 240, 58, 72, 160, 600, 36, 160, 70, 400, 60, 120, 36, 12500, 120, 128, 66, 440, 56, 240, 82, 600, 72

Offset

1,2

Links

Table of n, a(n) for n=1..73.

Index entries for sequences computed from indices in prime factorization

Formula

Multiplicative with a(p^e) = (q-1) * q^(e-1) where q = A003627(1+n) if p = A003627(n), otherwise q = p.

a(n) = A000010(A354091(n)).

a(n) = Sum_{d|n} A008683(n/d) * A354091(d).

For all n >= 1, A010872(a(n)) = A010872(A000010(n)) = A074942(n).

For all n >= 1, A007949(a(n)) = A007949(A000010(n)) = A354099(n).

Prog

(PARI) A354094(n) = { my(f=factor(n)); for(k=1, #f~, if(2==(f[k, 1]%3), for(i=1+primepi(f[k, 1]), oo, if(2==(prime(i)%3), f[k, 1]=prime(i); break)))); eulerphi(factorback(f)); };

Crossrefs

Möbius transform of A354091.

Cf. A000010, A003627, A007949, A008683, A010872, A074942, A354099.

Cf. also A003972.

Sequence in context: A177248 A191706 A081797 * A347590 A016517 A157407

Adjacent sequences: A354091 A354092 A354093 * A354095 A354096 A354097

Keyword

nonn,mult

Author

Antti Karttunen, May 17 2022

Status

approved