OFFSET
1,2
LINKS
Seiichi Manyama, Table of n, a(n) for n = 1..1000
EXAMPLE
Row 6 of Pascal's triangle is 1,6,15,20,15,6,1. The greatest common divisors of n and each integer from 1 to 6 are gcd(1,6)=1, gcd(2,6)=2, gcd(3,6)=3, gcd(4,6)=2, gcd(5,6)=1, and gcd(6,6)=6. So a(6) = (1/6)*( 6*1 + 15*2 + 20*3 + 15*2 + 6*1 + 1*6) = 138/6 = 23. Note that each term of the sum in parentheses is a multiple of 6, so 138 is a multiple of 6.
MAPLE
A159068 := proc(n) add(binomial(n, k)*gcd(k, n), k=1..n) ; end: A159069 := proc(n) A159068(n)/n ; end: seq(A159069(n), n=1..80) ; # R. J. Mathar, Apr 06 2009
MATHEMATICA
Table[Sum[Binomial[n, k] GCD[k, n], {k, n}]/n, {n, 34}] (* Michael De Vlieger, Aug 29 2017 *)
PROG
(PARI) a(n) = sum(k=1, n, binomial(n, k) * gcd(k, n))/n; \\ Michel Marcus, Aug 30 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
Leroy Quet, Apr 04 2009
EXTENSIONS
Extended by R. J. Mathar, Apr 06 2009
STATUS
approved