A062949 Multiplicative with a(p^e) = ((e+1)*p^(e+1)-(e+2)*p^e+1)/(p-1).

1, 3, 5, 9, 9, 15, 13, 25, 23, 27, 21, 45, 25, 39, 45, 65, 33, 69, 37, 81, 65, 63, 45, 125, 69, 75, 95, 117, 57, 135, 61, 161, 105, 99, 117, 207, 73, 111, 125, 225, 81, 195, 85, 189, 207, 135, 93, 325, 139, 207, 165, 225, 105, 285, 189, 325, 185, 171, 117, 405

Offset: 1

Author

Vladeta Jovovic, Jul 21 2001

Keywords

• nonn
• easy
• mult

Comments

Inverse Mobius transform of A062355.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A057660, A029939.

Programs

Maple

A062949 := proc(n) add(numtheory[phi](d)*numtheory[tau](d), d=numtheory[divisors](n)) ; end proc: # R. J. Mathar, Feb 09 2011

Mathematica

f[p_, e_] := ((e+1)*p^(e+1)-(e+2)*p^e+1)/(p-1); a[1] = 1; a[n_] := Times @@ (f @@@ FactorInteger[n]); Array[a, 60] (* Amiram Eldar, Jul 31 2019 *)

Formula

a(n) = Sum_{d|n} phi(d)*tau(d).

a(n) = Sum_{k=1..n} tau(n/gcd(n, k)).

a(n) = Sum_{d|n} d*uphi(n/d), where uphi() = A047994(). - Vladeta Jovovic, Mar 16 2004