A261768 a(n) = phi(n)^n - n^phi(n), where phi(n) is Euler's totient function.

0, -1, -1, 0, 399, 28, 162287, 61440, 9546255, 1038576, 74062575399, 16756480, 83695120256591, 78356634560, 35181809198207, 281470681743360, 246486713303685957375, 101559922656192, 604107995057426434824791, 1152921479006846976

Offset: 1

Author

Ilya Gutkovskiy, Aug 31 2015

Keywords

• sign

Comments

a(n) < n^n/e. If n is prime, a(n)/n^n = (1-1/n)^n - 1/n -> 1/e as n -> infinity. - Robert Israel, Sep 18 2015

Links

• Robert Israel, Table of n, a(n) for n = 1..388
• Eric Weisstein's World of Mathematics, Totient Function

Crossrefs

Cf. A000010, A062981.

Programs

Magma

[EulerPhi(n)^n-n^EulerPhi(n): n in [1..20]]; // Vincenzo Librandi, Sep 01 2015

Maple

seq(numtheory:-phi(n)^n - n^numtheory:-phi(n),n=1..30); # Robert Israel, Sep 18 2015

Mathematica

Table[EulerPhi[n]^n - n^EulerPhi[n], {n, 1, 20}]

PARI

a(n) = eulerphi(n)^n - n^eulerphi(n) \\ Anders Hellström, Aug 31 2015

Formula

a(n) = A000010(n)^n - n^A000010(n) = A000010(n)^n - A062981(n).