OFFSET
1,2
LINKS
Eric M. Schmidt, Table of n, a(n) for n = 1..1000
FORMULA
a(n) = n^4 * Product_{p prime, p|n} (1-1/p^2)*(1-1/p) * sigma(n)*phi(n).
From Amiram Eldar, Oct 30 2022: (Start)
Multiplicative with a(p^e) = (p^(e+1)-1) * (p-1)^2 * (p+1) * p^(5*e-4).
Sum_{k=1..n} a(k) ~ c * n^7, where c = (1/7) * Product_{p prime} (1 - 1/p^2 - 2/p^3 + 3/p^4 - 1/p^5) = 0.07103214283... . (End)
MATHEMATICA
a[n_] := n^4*DivisorSigma[1, n]*EulerPhi[n]*Product[(1-1/p^2)*(1-1/p), {p, FactorInteger[n][[All, 1]]}]; a[1]=1; Table[a[n], {n, 1, 30}] (* Jean-François Alcover, May 02 2013, after Eric M. Schmidt *)
PROG
(Sage)
def A070943(n) : return Integer(n^4 * sigma(n) * euler_phi(n) * prod((1-1/p^2)*(1-1/p) for (p, m) in factor(n))) # Eric M. Schmidt, May 02 2013
CROSSREFS
KEYWORD
mult,nonn
AUTHOR
Yuval Dekel (dekelyuval(AT)hotmail.com), Sep 12 2003
EXTENSIONS
More terms from Benoit Cloitre, Sep 13 2003
More terms from Eric M. Schmidt, May 02 2013
STATUS
approved