A354204 - OEIS

%I #6 May 23 2022 17:45:53

%S 1,4,6,20,12,24,10,100,42,48,18,120,16,40,72,500,28,168,22,240,60,72,

%T 30,600,156,64,294,200,36,288,42,2500,108,112,120,840,40,88,96,1200,

%U 52,240,46,360,504,120,58,3000,110,624,168,320,60,1176,216,1000,132,144,66,1440,72,168,420,12500,192,432,70,560,180

%N a(n) = phi(A354202(n)), where A354202 is fully multiplicative with a(p) = A354200(A000720(p)).

%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 = A354200(A000720(p)).

%F a(n) = A000010(A354202(n)).

%F a(n) = Sum_{d|n} A008683(n/d) * A354202(d).

%o (PARI)

%o A354200(n) = if(1==n,5,my(p=prime(n), m=p%4); forprime(q=1+p,,if(m==(q%4),return(q))));

%o A354204(n) = { my(f=factor(n)); for(k=1,#f~,f[k,1] = A354200(primepi(f[k,1]))); eulerphi(factorback(f)); };

%o \\ Alternatively:

%o A354204v2(n) = { my(f=factor(n),q); prod(k=1,#f~,q = A354200(primepi(f[k,1])); (q-1)*(q^(f[k,2]-1))); };

%Y Möbius transform of A354202.

%Y Cf. A000010, A008683, A354200, A354205.

%K nonn,mult

%O 1,2

%A _Antti Karttunen_, May 23 2022