A271440 a(n) = sigma(prime(n)^n) - phi(prime(n)^n).

2, 7, 56, 743, 30746, 773527, 49783736, 1837403019, 160181560802, 29532404308019, 1666577516860962, 360777399719461393, 45691067858241526814, 3477439299142731351087, 518913689466371066697746, 147680787468230866751370317, 43490064769447225534580532962

Offset: 1

Author

Wesley Ivan Hurt, Apr 07 2016

Keywords

• nonn
• easy

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..303

Crossrefs

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

Programs

Maple

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

Mathematica

Table[DivisorSigma[1, Prime[n]^n] - EulerPhi[Prime[n]^n], {n, 20}]
DivisorSigma[1,#]-EulerPhi[#]&/@Table[Prime[n]^n,{n,20}] (* Harvey P. Dale, Feb 07 2025 *)

PARI

a(n) = sigma(prime(n)^n) - eulerphi(prime(n)^n); \\ Altug Alkan, Apr 08 2016

Formula

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

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

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