A353767 a(n) = phi(sigma(A003961(n))), where A003961 is fully multiplicative with a(p) = nextprime(p).

1, 2, 2, 12, 4, 8, 4, 16, 30, 16, 6, 24, 6, 16, 16, 110, 8, 60, 8, 48, 24, 24, 8, 64, 36, 24, 48, 48, 16, 64, 18, 144, 24, 32, 32, 360, 12, 32, 36, 128, 20, 96, 16, 72, 120, 32, 18, 220, 108, 72, 32, 72, 16, 192, 48, 128, 48, 64, 30, 192, 32, 72, 120, 1092, 48, 96, 24, 96, 48, 128, 36, 480, 32, 48, 108, 96, 48, 144

Offset: 1

Author

Antti Karttunen, May 10 2022

Keywords

• nonn

Links

• Index entries for sequences computed from indices in prime factorization
• Index entries for sequences related to sigma(n)

Crossrefs

Cf. A000010, A000203, A003961, A003973, A062401, A326042, A353790.

Programs

Mathematica

f[p_, e_] := NextPrime[p]^e; s[1] = 1; s[n_] := Times @@ f @@@ FactorInteger[n]; a[n_] := EulerPhi[DivisorSigma[1, s[n]]]; Array[a, 100] (* Amiram Eldar, May 10 2022 *)

PARI

A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
A353767(n) = eulerphi(sigma(A003961(n)));

Formula

a(n) = A000010(A003973(n)) = A062401(A003961(n)) = A000010(A000203(A003961(n))).

a(n) = A353790(n) / A326042(n).