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A145353 Sum of the number of e-divisors of all numbers from 1 up to n. 5
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, 36, 38, 40, 41, 42, 43, 45, 46, 47, 48, 52, 53, 54, 55, 57, 58, 59, 60, 62, 64, 65, 66, 69, 71, 73, 74, 76, 77, 79, 80, 82, 83, 84, 85, 87, 88, 89, 91, 95, 96, 97, 98, 100, 101, 102, 103, 107 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
LINKS
J. Wu, Problème de diviseurs exponentiels et entiers exponentiellement sans facteur carré, J. Theor. Nombr. Bordeaux 7 (1) (1995) 133-141.
FORMULA
a(n) ~ c * n, where c = A327837. - Amiram Eldar, Dec 08 2022
MATHEMATICA
f[p_, e_] := DivisorSigma[0, e]; ediv[n_] := Times @@ (f @@@ FactorInteger[n]); Accumulate[Array[ediv, 100]] (* Amiram Eldar, Jun 23 2019 *)
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.
Different from A013936 (which does not contain 52).
Sequence in context: A179813 A191914 A329898 * A013936 A229992 A076437
KEYWORD
nonn
AUTHOR
STATUS
approved

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Last modified May 20 06:19 EDT 2024. Contains 372703 sequences. (Running on oeis4.)