OFFSET
1,2
LINKS
Harry J. Smith, Table of n, a(n) for n = 1..1000
FORMULA
a(n) = Sum_{d|n} d*tau(d^2).
Multiplicative with a(p^e) = (p^(e+2) - 3*p^(e+1) + p + 1 + 2*p^(e+2)*e - 2*p^(e+1)*e)/(p-1)^2.
MATHEMATICA
a[n_]:= Sum[LCM[i, j], {i, Divisors[n]}, {j, Divisors[n]}];
Array[a, 60] (* Jean-François Alcover, Jun 03 2019 *)
f[p_, e_] := (p^(e+2) - 3*p^(e+1) + p + 1 + 2*p^(e+2)*e - 2*p^(e+1)*e)/(p-1)^2; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 60] (* Amiram Eldar, Aug 28 2023 *)
PROG
(PARI) for (n=1, 1000, d=divisors(n); a=sum(i=1, length(d), numdiv(d[i]^2)*d[i]); write("b064950.txt", n, " ", a)) \\ Harry J. Smith, Oct 01 2009
(SageMath)
def A064950(n) :
tau = sloane.A000005; D = divisors(n)
return reduce(lambda x, y: x+y, [d*tau(d^2) for d in D])
[A064950(n) for n in (1..54)] # Peter Luschny, Sep 10 2012
CROSSREFS
KEYWORD
mult,nonn,easy
AUTHOR
Vladeta Jovovic, Oct 28 2001
STATUS
approved
