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a(n) = phi(sigma(A003961(n))), where A003961 is fully multiplicative with a(p) = nextprime(p).
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%I #8 May 10 2022 16:40:22

%S 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,

%T 48,48,16,64,18,144,24,32,32,360,12,32,36,128,20,96,16,72,120,32,18,

%U 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

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

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

%H <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>

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

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

%t 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 *)

%o (PARI)

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

%o A353767(n) = eulerphi(sigma(A003961(n)));

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

%K nonn

%O 1,2

%A _Antti Karttunen_, May 10 2022