OFFSET
1,2
COMMENTS
A number of conjectures are possible, many of which should be easy to prove. Examples: (1) If n is a product of two primes then a(n)=13. (2) If n is a square of a prime then a(n)=6. - John W. Layman, Sep 01 2003
LINKS
Antti Karttunen, Table of n, a(n) for n = 1..10000
FORMULA
For a prime p, a(p) = 3.
MATHEMATICA
f1[p_, e_] := (e+1)^3 - e^3; f2[p_, e_] := 2*e + 1; a[1] = 1; a[n_] := (Times @@ f1 @@@ (f = FactorInteger[n]) + 3 * Times @@ f2 @@@f + 2) / 6; Array[a, 100] (* Amiram Eldar, Sep 03 2023 *)
PROG
(PARI)
A048691(n) = numdiv(n^2);
A070919(n) = sumdiv(n, d, (numdiv(d)^3)*moebius(n/d));
A086222(n) = ((A070919(n)+3*A048691(n)+2)/6); \\ Antti Karttunen, May 19 2017, after Jovovic's formula.
(PARI) a(n) = {my(e = factor(n)[, 2]); (vecprod(apply(x->(x+1)^3-x^3, e)) + 3*vecprod(apply(x->2*x+1, e)) + 2) / 6; } \\ Amiram Eldar, Sep 03 2023
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Yuval Dekel (dekelyuval(AT)hotmail.com), Aug 28 2003
EXTENSIONS
More terms from John W. Layman, Sep 01 2003
STATUS
approved