The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A083913 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A083913

Number of divisors of n that are congruent to 3 modulo 10.
(history; published version)

#13 by OEIS Server at Sat Dec 30 05:11:54 EST 2023

LINKS

Amiram Eldar, <a href="/A083913/b083913_1.txt">Table of n, a(n) for n = 1..10000</a>

#12 by Alois P. Heinz at Sat Dec 30 05:11:54 EST 2023

STATUS

reviewed

approved

Discussion

Sat Dec 30

05:11

OEIS Server: Installed first b-file as b083913.txt.

#11 by Joerg Arndt at Sat Dec 30 03:27:47 EST 2023

STATUS

proposed

reviewed

#10 by Amiram Eldar at Sat Dec 30 03:05:31 EST 2023

STATUS

editing

proposed

#9 by Amiram Eldar at Sat Dec 30 02:37:06 EST 2023

LINKS

Amiram Eldar, <a href="/A083913/b083913_1.txt">Table of n, a(n) for n = 1..10000</a>

MATHEMATICA

a[n_] := DivisorSum[n, 1 &, Mod[#, 10] == 3 &]; Array[a, 100] (* Amiram Eldar, Dec 30 2023 *)

PROG

(PARI) a(n) = sumdiv(n, d, d % 10 == 3); \\ Amiram Eldar, Dec 30 2023

#8 by Amiram Eldar at Sat Dec 30 02:35:56 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.

FORMULA

Sum_{k=1..n} a(k) = n*log(n)/10 + c*n + O(n^(1/3)*log(n)), where c = gamma(3,10) - (1 - gamma)/10 = 0.07771547..., gamma(3,10) = -(psi(3/10) + log(10))/10 is a generalized Euler constant, and gamma is Euler's constant (A001620) (Smith and Subbarao, 1981). - Amiram Eldar, Dec 30 2023

CROSSREFS

Cf. A010879, A000005, A001227, A010879.

Cf. A001620, A002392, A354642 (psi(3/10)).

Cf. A083910, A083911, A083912, A083914, A083915, A083916, A083917, A083918, A083919.

KEYWORD

nonn,easy

STATUS

approved

editing

#7 by Bruno Berselli at Wed Sep 11 11:12:57 EDT 2019

STATUS

proposed

approved

#6 by Ilya Gutkovskiy at Wed Sep 11 10:03:55 EDT 2019

STATUS

editing

proposed

#5 by Ilya Gutkovskiy at Wed Sep 11 09:59:59 EDT 2019

COMMENTS

a(n) = A000005(n) - A083910(n) - A083911(n) - A083912(n) - A083914(n) - A083915(n) - A083916(n) - A083917(n) - A083918(n) - A083919(n).

FORMULA

a(n) = A000005(n) - A083910(n) - A083911(n) - A083912(n) - A083914(n) - A083915(n) - A083916(n) - A083917(n) - A083918(n) - A083919(n).

#4 by Ilya Gutkovskiy at Wed Sep 11 09:53:28 EDT 2019

FORMULA

G.f.: Sum_{k>=1} x^(3*k)/(1 - x^(10*k)). - Ilya Gutkovskiy, Sep 11 2019

STATUS

approved

editing