A085730 Euler's totient function applied to the sequence of prime powers.

1, 1, 2, 2, 4, 6, 4, 6, 10, 12, 8, 16, 18, 22, 20, 18, 28, 30, 16, 36, 40, 42, 46, 42, 52, 58, 60, 32, 66, 70, 72, 78, 54, 82, 88, 96, 100, 102, 106, 108, 112, 110, 100, 126, 64, 130, 136, 138, 148, 150, 156, 162, 166, 156, 172, 178, 180, 190, 192, 196, 198, 210

Offset

1,3

Comments

a(n) = A000010(A000961(n)).

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Eric Weisstein's World of Mathematics, Prime Power.

Eric Weisstein's World of Mathematics, Totient Function.

Formula

a(p^e) = (p-1)*p^(e-1).

a(n) = (A025473(n)-1)*A025473(n)^(A025474(n)-1).

Prog

(Haskell)
a085730 1 = 1
a085730 n = (p - 1) * p ^ (e - 1)
   where p =  a025473 n; e =  a025474 n
-- Reinhard Zumkeller, Feb 16 2012
(PARI) list(lim)=my(v=List(primes(primepi(lim)))); listput(v, 1); for(e=2, log(lim+.5)\log(2), forprime(p=2, (lim+.5)^(1/e), listput(v, p^e))); apply(n->eulerphi(n), vecsort(Vec(v))) \\ Charles R Greathouse IV, Apr 30 2012

Crossrefs

Cf. A000010, A000961, A025473, A025474, A207193.

Sequence in context: A166362 A050469 A350229 * A232065 A219741 A210603

Adjacent sequences: A085727 A085728 A085729 * A085731 A085732 A085733

Keyword

nonn

Author

Reinhard Zumkeller, Jul 20 2003

Status

approved