A062949 - OEIS

%I #17 Aug 31 2023 03:48:25

%S 1,3,5,9,9,15,13,25,23,27,21,45,25,39,45,65,33,69,37,81,65,63,45,125,

%T 69,75,95,117,57,135,61,161,105,99,117,207,73,111,125,225,81,195,85,

%U 189,207,135,93,325,139,207,165,225,105,285,189,325,185,171,117,405

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

%C Inverse Mobius transform of A062355.

%H Amiram Eldar, <a href="/A062949/b062949.txt">Table of n, a(n) for n = 1..10000</a>

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

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

%F a(n) = Sum_{d|n} d*uphi(n/d), where uphi() = A047994(). - _Vladeta Jovovic_, Mar 16 2004

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

%t 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 *)

%Y Cf. A057660, A029939.

%K nonn,easy,mult

%O 1,2

%A _Vladeta Jovovic_, Jul 21 2001