OFFSET
1,2
LINKS
Alois P. Heinz, Table of n, a(n) for n = 1..1000
Richard Bellman and Harold N. Shapiro, On a problem in additive number theory, Annals Math., Vol. 49, No. 2 (1948), 333-340. See Eq. 1.6. [From N. J. A. Sloane, Mar 12 2009]
Paul Erdős, On the sum Sum_{n=1..x} d[d(n)], Math. Student, Vol. 36 (1968), pp. 227-229.
E. Heppner, Über die Iteration von Teilerfunktionen, Journal für die reine und angewandte Mathematik, Vol. 265 (1974), pp. 176-182.
FORMULA
a(n) = b * n * log(log(n)) + Sum_{k=0..floor(sqrt(n))} b_k * n/log(n)^k + O(n * exp(-c*sqrt(log(n)))), where b, b_k and c are constants (Heppner, 1974). - Amiram Eldar, Jan 15 2024
MAPLE
with(numtheory): a:= n-> add(tau(tau (k)), k=1..n): seq(a(n), n=1..70); # Alois P. Heinz, Aug 28 2008
MATHEMATICA
Table[Sum[DivisorSigma[0, DivisorSigma[0, k]], {k, 1, n}], {n, 1, 62}] (* Geoffrey Critzer, Sep 28 2013 *)
Accumulate[Table[DivisorSigma[0, DivisorSigma[0, k]], {k, 1, 62}]] (* Amiram Eldar, Jan 15 2024 *)
PROG
(PARI) a(n) = sum(k = 1, n, numdiv(numdiv(k))); \\ Michel Marcus, Sep 28 2013
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Leroy Quet, Jun 05 2008
EXTENSIONS
More terms from Alois P. Heinz, Aug 28 2008
STATUS
approved