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a(n) = sigma(prime(n)^n) - phi(prime(n)^n).
1

%I #7 Apr 09 2016 16:11:40

%S 2,7,56,743,30746,773527,49783736,1837403019,160181560802,

%T 29532404308019,1666577516860962,360777399719461393,

%U 45691067858241526814,3477439299142731351087,518913689466371066697746,147680787468230866751370317,43490064769447225534580532962

%N a(n) = sigma(prime(n)^n) - phi(prime(n)^n).

%F a(n) = (2*prime(n)^n-prime(n)^(n-1)-1) / (prime(n)-1).

%F a(n) = (prime(n)^(n+1)-prime(n)^(n-1)*(prime(n)-1)^2-1) / (prime(n)-1).

%F a(n) = A051612(A062457(n)) = A000203(A062457(n)) - A000010(A062457(n)).

%p with(numtheory): A271440:=n->sigma(ithprime(n)^n)-phi(ithprime(n)^n): seq(A271440(n), n=1..30);

%t Table[DivisorSigma[1, Prime[n]^n] - EulerPhi[Prime[n]^n], {n, 20}]

%o (PARI) a(n) = sigma(prime(n)^n) - eulerphi(prime(n)^n); \\ _Altug Alkan_, Apr 08 2016

%Y Cf. A000010 (phi), A000040 (primes), A000203 (sigma), A051612, A062457.

%K nonn,easy

%O 1,1

%A _Wesley Ivan Hurt_, Apr 07 2016