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A261768
a(n) = phi(n)^n - n^phi(n), where phi(n) is Euler's totient function.
1
0, -1, -1, 0, 399, 28, 162287, 61440, 9546255, 1038576, 74062575399, 16756480, 83695120256591, 78356634560, 35181809198207, 281470681743360, 246486713303685957375, 101559922656192, 604107995057426434824791, 1152921479006846976
OFFSET
1,5
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
Eric Weisstein's World of Mathematics, Totient Function
FORMULA
a(n) = A000010(n)^n - n^A000010(n) = A000010(n)^n - A062981(n).
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}]
PROG
(PARI) a(n) = eulerphi(n)^n - n^eulerphi(n) \\ Anders Hellström, Aug 31 2015
(Magma) [EulerPhi(n)^n-n^EulerPhi(n): n in [1..20]]; // Vincenzo Librandi, Sep 01 2015
CROSSREFS
Sequence in context: A235958 A187515 A235569 * A274446 A253598 A046013
KEYWORD
sign
AUTHOR
Ilya Gutkovskiy, Aug 31 2015
STATUS
approved