A099593 Sum of the number of e-divisors of all numbers from 2 up to n.

0, 1, 2, 4, 5, 6, 7, 9, 11, 12, 13, 15, 16, 17, 18, 21, 22, 24, 25, 27, 28, 29, 30, 32, 34, 35, 37, 39, 40, 41, 42, 44, 45, 46, 47, 51, 52, 53, 54, 56, 57, 58, 59, 61, 63, 64, 65, 68, 70, 72, 73, 75, 76, 78, 79, 81, 82, 83, 84, 86, 87, 88, 90, 94, 95, 96, 97, 99, 100, 101

Offset: 1

Author

Ralf Stephan, Oct 26 2004

Keywords

• nonn

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• J. Wu, Problème de diviseurs exponentiels et entiers exponentiellement sans facteur carré, J. Theor. Nombr. Bordeaux 7 (1) (1995) 133-141.

Crossrefs

Equals - 1 + partial sums of A049419. Cf. A145353, A327837.

Programs

Mathematica

f[p_, e_]  := DivisorSigma[0, e]; ediv[n_] := Times @@ (f @@@ FactorInteger[n]);
Accumulate[Array[ediv, 100]] - 1 (* Amiram Eldar, Jun 23 2019 *)

Formula

a(n) ~ A327837 * n. - Vaclav Kotesovec, Feb 27 2023