OFFSET
1,2
COMMENTS
Conjecture: this is the third inverse Mobius transform of the sequence 4^A001221(n). - R. J. Mathar, Aug 09 2012
LINKS
FORMULA
a(n) = Sum_{i|n, j|n} tau(i)*tau(j)/tau(gcd(i, j)), where tau(n) = number of divisors of n, cf. A000005.
Also a(n) = Sum_{i|n, j|n} tau(lcm(i, j)).
a(n) = Sum_{d|n} tau_3(d^2) = Sum_{d|n} A007425(d^2). - Enrique Pérez Herrero, Jan 17 2013
MATHEMATICA
f[p_, e_] := (e+1)*(e+2)*(4*e+3)/6; a[n_] := Times @@ f @@@ FactorInteger[n]; a[1] = 1; Array[a, 100] (* Amiram Eldar, Sep 05 2023 *)
PROG
(Scheme, with memoization-macro definec) (definec (A062368 n) (if (= 1 n) n (let ((e (A067029 n))) (* 1/6 (+ 1 e) (+ 2 e) (+ 3 (* 4 e)) (A062368 (A028234 n)))))) ;; Antti Karttunen, Nov 24 2017
CROSSREFS
KEYWORD
nonn,easy,mult
AUTHOR
Vladeta Jovovic, Jul 07 2001
STATUS
approved