The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A083910 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A083910

Number of divisors of n that are congruent to 0 modulo 10.
(history; published version)

#26 by Michael De Vlieger at Sat Dec 30 09:33:46 EST 2023

STATUS

reviewed

approved

#25 by Joerg Arndt at Sat Dec 30 03:27:58 EST 2023

STATUS

proposed

reviewed

#24 by Amiram Eldar at Sat Dec 30 03:05:25 EST 2023

STATUS

editing

proposed

#23 by Amiram Eldar at Sat Dec 30 03:04:23 EST 2023

FORMULA

Sum_{k=1..n} a(k) = n*log(n)/10 + c*n + O(n^(1/3)*log(n)), where c = (2*gamma - 1 - log(10))/10 = -0.214815..., where and gamma is Euler's constant (A001620) (Smith and Subbarao, 1981). - Amiram Eldar, Dec 30 2023

#22 by Amiram Eldar at Sat Dec 30 02:34:27 EST 2023

LINKS

R. A. Smith and M. V. Subbarao, <a href="https://doi.org/10.4153/CMB-1981-005-3">The average number of divisors in an arithmetic progression</a>, Canadian Mathematical Bulletin, Vol. 24, No. 1 (1981), pp. 37-41.

#21 by Amiram Eldar at Sat Dec 30 02:33:11 EST 2023

CROSSREFS

Cf. A010879, A000005, A001227, A183063, A000007, A001227, A010879, A027750, A183063.

#20 by Amiram Eldar at Sat Dec 30 02:28:54 EST 2023

MATHEMATICA

a[n_] := If[Divisible[n, 10], DivisorSigma[0, n/10], 0]; Array[a, 100] (* Amiram Eldar, Dec 30 2023 *)

#19 by Amiram Eldar at Sat Dec 30 02:27:24 EST 2023

FORMULA

Sum_{k=1..n} a(k) = n*log(n)/10 + c*n + O(n^(1/3)*log(n)), where c = (2*gamma - 1 - log(10))/10 = -0.214815..., where gamma is Euler's constant (A001620) (Smith and Subbarao, 1981). - Amiram Eldar, Dec 30 2023

CROSSREFS

Cf. A001620, A002392.

Cf. A083911, A083912, A083913, A083914, A083915, A083916, A083917, A083918, A083919.

KEYWORD

nonn,easy

STATUS

approved

editing

#18 by Bruno Berselli at Wed Sep 11 11:12:07 EDT 2019

STATUS

proposed

approved

#17 by Ilya Gutkovskiy at Wed Sep 11 10:04:06 EDT 2019

STATUS

editing

proposed