The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A145353 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A145353

Sum of the number of e-divisors of all numbers from 1 up to n.
(history; published version)

#13 by Michael De Vlieger at Thu Dec 08 07:36:33 EST 2022

STATUS

reviewed

approved

#12 by Joerg Arndt at Thu Dec 08 02:38:57 EST 2022

STATUS

proposed

reviewed

#11 by Amiram Eldar at Thu Dec 08 02:32:43 EST 2022

STATUS

editing

proposed

#10 by Amiram Eldar at Thu Dec 08 02:25:12 EST 2022

FORMULA

a(n) ~ c * n, where c = A327837. - Amiram Eldar, Dec 08 2022

PROG

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

lista(nmax) = {my(s = 0); for(n = 1, nmax, s += d(n); print1(s, ", ")); } \\ Amiram Eldar, Dec 08 2022

CROSSREFS

Equals partial sums of A049419. Cf. A099353.

Cf. A099353, A327837.

STATUS

approved

editing

#9 by Alois P. Heinz at Sun Jun 23 17:50:01 EDT 2019

STATUS

proposed

approved

#8 by Amiram Eldar at Sun Jun 23 17:38:14 EDT 2019

STATUS

editing

proposed

#7 by Amiram Eldar at Sun Jun 23 17:35:32 EDT 2019

LINKS

Amiram Eldar, <a href="/A145353/b145353.txt">Table of n, a(n) for n = 1..10000</a>

MATHEMATICA

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

STATUS

approved

editing

#6 by Bruno Berselli at Wed May 09 03:12:47 EDT 2018

STATUS

proposed

approved

#5 by Michel Marcus at Wed May 09 02:02:19 EDT 2018

STATUS

editing

proposed

#4 by Michel Marcus at Wed May 09 02:02:08 EDT 2018

LINKS

J. Wu, <a href="http://wwwdx.emisdoi.de/journals/JTNBorg/1995-110.5802/jtnb7-1_englishjtnb.html#jourelec136">Probleme Problème de diviseurs exponentiels... et entiers exponentiellement sans facteur carré</a>, J. Theor. Nombr. Bordeaux 7 (1) (1995) 133-141.

STATUS

approved

editing

Discussion

Wed May 09

02:02

Michel Marcus: better link