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

%I #12 Feb 27 2023 13:26:43

%S 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,

%T 35,37,39,40,41,42,44,45,46,47,51,52,53,54,56,57,58,59,61,63,64,65,68,

%U 70,72,73,75,76,78,79,81,82,83,84,86,87,88,90,94,95,96,97,99,100,101

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

%H Amiram Eldar, <a href="/A099593/b099593.txt">Table of n, a(n) for n = 1..10000</a>

%H J. Wu, <a href="http://dx.doi.org/10.5802/jtnb.136">Problème de diviseurs exponentiels et entiers exponentiellement sans facteur carré</a>, J. Theor. Nombr. Bordeaux 7 (1) (1995) 133-141.

%F a(n) ~ A327837 * n. - _Vaclav Kotesovec_, Feb 27 2023

%t f[p_, e_] := DivisorSigma[0, e]; ediv[n_] := Times @@ (f @@@ FactorInteger[n]);

%t Accumulate[Array[ediv, 100]] - 1 (* _Amiram Eldar_, Jun 23 2019 *)

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

%K nonn

%O 1,3

%A _Ralf Stephan_, Oct 26 2004

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Last modified April 25 03:15 EDT 2024. Contains 371964 sequences. (Running on oeis4.)