OFFSET
0,3
COMMENTS
Consider the triangle T(n, k) = A003989(n, k) = gcd(n-k+1, k), n >= 1, k = 1..n. Then a(n) = Sum_{k=0..floor(n/2)} T(n-k+1, k+1), for n >= 0. - R. J. Mathar, May 11 2018 [adjusted to the definition of A003989. - Wolfdieter Lang, May 12 2018]
LINKS
Robert Israel, Table of n, a(n) for n = 0..10000
FORMULA
a(n) = Sum_{k=0..floor(n/2)} gcd(n-2*k+1, k+1). [corrected by R. J. Mathar, May 11 2018]
MAPLE
f:= n -> add(igcd(n-2*k+1, k+1), k=0..n/2):
map(f, [$0..100]); # Robert Israel, May 11 2018
MATHEMATICA
Array[Sum[GCD[# - 2 k + 1, k + 1], {k, 0, Floor[#/2]}] &, 61, 0] (* Michael De Vlieger, May 14 2018 *)
PROG
(PARI) a(n) = sum(k=0, n\2, gcd(n-2*k+1, k+1)); \\ Michel Marcus, May 11 2018
(GAP) Flat(List([0..70], n->Sum([0..Int(n/2)], k->Gcd(n-2*k+1, k+1)))); # Muniru A Asiru, May 15 2018
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, May 03 2005
EXTENSIONS
Name corrected by R. J. Mathar, May 11 2018
STATUS
approved