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A139130 a(n) = Sum_{k=1..n} d(d(k)), where d(k) = number of divisors of k. 2
1, 3, 5, 7, 9, 12, 14, 17, 19, 22, 24, 28, 30, 33, 36, 38, 40, 44, 46, 50, 53, 56, 58, 62, 64, 67, 70, 74, 76, 80, 82, 86, 89, 92, 95, 98, 100, 103, 106, 110, 112, 116, 118, 122, 126, 129, 131, 135, 137, 141, 144, 148, 150, 154, 157, 161, 164, 167, 169, 175, 177, 180 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
LINKS
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
Sequence in context: A198082 A082767 A047932 * A219087 A186705 A361512
KEYWORD
nonn,easy
AUTHOR
Leroy Quet, Jun 05 2008
EXTENSIONS
More terms from Alois P. Heinz, Aug 28 2008
STATUS
approved

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Last modified February 24 14:59 EST 2024. Contains 370305 sequences. (Running on oeis4.)