%I #13 Dec 08 2022 07:36:33

%S 1,2,3,5,6,7,8,10,12,13,14,16,17,18,19,22,23,25,26,28,29,30,31,33,35,

%T 36,38,40,41,42,43,45,46,47,48,52,53,54,55,57,58,59,60,62,64,65,66,69,

%U 71,73,74,76,77,79,80,82,83,84,85,87,88,89,91,95,96,97,98,100,101,102,103,107

%N Sum of the number of e-divisors of all numbers from 1 up to n.

%H Amiram Eldar, <a href="/A145353/b145353.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) ~ c * n, where c = A327837. - _Amiram Eldar_, Dec 08 2022

%t f[p_, e_] := DivisorSigma[0, e]; ediv[n_] := Times @@ (f @@@ FactorInteger[n]); Accumulate[Array[ediv, 100]] (* _Amiram Eldar_, Jun 23 2019 *)

%o (PARI) d(n) = {my(f = factor(n)); prod(i = 1, #f~, numdiv(f[i,2]));}

%o lista(nmax) = {my(s = 0); for(n = 1, nmax, s += d(n); print1(s, ", ")); } \\ _Amiram Eldar_, Dec 08 2022

%Y Equals partial sums of A049419.

%Y Cf. A099353, A327837.

%Y Different from A013936 (which does not contain 52).

%K nonn

%O 1,2

%A _Jaroslav Krizek_ and _N. J. A. Sloane_, Mar 03 2009