A354094 - OEIS

%I #9 May 17 2022 17:50:26

%S 1,4,2,20,10,8,6,100,6,40,16,40,12,24,20,500,22,24,18,200,12,64,28,

%T 200,110,48,18,120,40,80,30,2500,32,88,60,120,36,72,24,1000,46,48,42,

%U 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

%N 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.

%H <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>

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

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

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

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

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

%o (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)); };

%Y Möbius transform of A354091.

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

%Y Cf. also A003972.

%K nonn,mult

%O 1,2

%A _Antti Karttunen_, May 17 2022