A364932 - OEIS

%I #21 Feb 13 2024 14:33:18

%S 1,2,2,2,2,4,4,4,4,6,4,8,6,8,8,8,6,12,8,12,16,12,8,16,8,12,12,16,8,24,

%T 16,16,16,18,16,24,18,16,24,24,12,32,20,24,24,24,16,32,24,24,24,24,18,

%U 36,24,32,32,24,16,48,30,32,32,32,24,48,32,36,32,48,24

%N a(n) = phi(psi(n)).

%C Here phi is Euler's totient function and psi is the Dedekind psi function.

%C Values of psi(n), n > 1 are always greater than n, while values of phi(n), n > 1 are always less than n.

%C a(39270) = 41472 is the first term where phi(psi(n)) exceeds n.

%H Robert Israel, <a href="/A364932/b364932.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = A000010(A001615(n)).

%F a(2^k) = A000010(2^k), k >= 2.

%p f:= proc(n) local p; numtheory:-phi(n * mul(1+1/p, p = numtheory:-factorset(n))) end proc:

%p map(f, [$1..100]); # _Robert Israel_, Feb 13 2024

%t a[n_] := EulerPhi[n*Times @@ (1 + 1/FactorInteger[n][[;; , 1]])]; a[1] = 1; Array[a, 100] (* _Amiram Eldar_, Aug 13 2023 *)

%o (Python)

%o from sympy.ntheory.factor_ import totient

%o from sympy import isprime, primefactors, prod

%o def psi(n):

%o     plist = primefactors(n)

%o     return n*prod(p+1 for p in plist)//prod(plist)

%o def a(n): return totient(psi(n))

%o (PARI) a(n) = eulerphi(n * sumdivmult(n, d, issquarefree(d)/d)); \\ _Michel Marcus_, Aug 13 2023

%Y Cf. A000010, A001615, A293713, A364631.

%K nonn,look

%O 1,2

%A _Torlach Rush_, Aug 13 2023