OFFSET
1,2
COMMENTS
Equals row sums of triangle A168534. - Gary W. Adamson, Nov 28 2009
LINKS
Alois P. Heinz, Table of n, a(n) for n = 1..1000
FORMULA
a(n) = Sum_{d|n} d * A000837(n/d).
a(n) = Sum_{d|n} phi(n/d)*numbpart(d) = Sum_{d|n} A000010(n/d)*A000041(d). - Vladeta Jovovic, May 08 2003
From Richard L. Ollerton, May 06 2021: (Start)
a(n) = Sum_{k=1..n} A000041(gcd(n,k)).
EXAMPLE
Partitions of 4 are 1+1+1+1, 1+1+2, 2+2, 1+3, 4, the corresponding GCD's of parts are 1,1,2,1,4 and their sum is a(4) = 9.
MAPLE
with(numtheory): with(combinat):
a:= n-> add(phi(n/d)*numbpart(d), d=divisors(n)):
seq(a(n), n=1..50); # Alois P. Heinz, Apr 02 2015
MATHEMATICA
a[n_] := Sum[EulerPhi[n/d]*PartitionsP[d], {d, Divisors[n]}]; Table[a[n], {n, 1, 50}] (* Jean-François Alcover, Jul 01 2015, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Vladeta Jovovic, Dec 24 2002
STATUS
approved