A065968 a(n) = n * Sum_{primes p dividing n} (1 - 1/p).

0, 1, 2, 2, 4, 7, 6, 4, 6, 13, 10, 14, 12, 19, 22, 8, 16, 21, 18, 26, 32, 31, 22, 28, 20, 37, 18, 38, 28, 59, 30, 16, 52, 49, 58, 42, 36, 55, 62, 52, 40, 85, 42, 62, 66, 67, 46, 56, 42, 65, 82, 74, 52, 63, 94, 76, 92, 85, 58, 118, 60, 91, 96, 32, 112

Offset

1,3

Comments

For a prime p, a(p) = phi(p), where phi is Euler's totient function. - Alonso del Arte, Jun 16 2012

Links

Harry J. Smith, Table of n, a(n) for n = 1..1000

Example

a(10) = 13 because 10 is divisible by the primes 2 and 5, and 10*(1/2 + 4/5) = 13.

Prog

(PARI) { for (n=1, 1000, s=0; p=2; while (p<=n, if(n%p == 0, s+=1 - 1/p); p=nextprime(p + 1)); write("b065968.txt", n, " ", n*s) ) } \\ Harry J. Smith, Nov 05 2009

Crossrefs

Cf. A000010 (same definition except for the crucial difference of product instead of sum for the 1 - 1/p).

Sequence in context: A270227 A162251 A244011 * A105669 A338917 A256963

Adjacent sequences: A065965 A065966 A065967 * A065969 A065970 A065971

Keyword

nonn

Author

N. J. A. Sloane, Dec 09 2001

Status

approved