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#15 by OEIS Server at Sat Dec 30 08:33:28 EST 2023
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| LINKS
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Amiram Eldar, <a href="/A083915/b083915_1.txt">Table of n, a(n) for n = 1..10000</a>
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#14 by Alois P. Heinz at Sat Dec 30 08:33:28 EST 2023
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Discussion
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| Sat Dec 30
| 08:33
| OEIS Server: Installed first b-file as b083915.txt.
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#13 by Joerg Arndt at Sat Dec 30 03:27:32 EST 2023
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#12 by Amiram Eldar at Sat Dec 30 03:05:32 EST 2023
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#11 by Amiram Eldar at Sat Dec 30 02:43:30 EST 2023
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#10 by Amiram Eldar at Sat Dec 30 02:42:57 EST 2023
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| LINKS
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Amiram Eldar, <a href="/A083915/b083915_1.txt">Table of n, a(n) for n = 1..10000</a>
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| MATHEMATICA
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a[n_] := DivisorSum[n, 1 &, Mod[#, 10] == 5 &]; Array[a, 100] (* Amiram Eldar, Dec 30 2023 *)
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| PROG
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(PARI) a(n) = sumdiv(n, d, d % 10 == 5); \\ Amiram Eldar, Dec 30 2023
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#9 by Amiram Eldar at Sat Dec 30 02:41:16 EST 2023
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| LINKS
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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.
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| FORMULA
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Sum_{k=1..n} a(k) = n*log(n)/10 + c*n + O(n^(1/3)*log(n)), where c = gamma(5,10) - (1 - gamma)/10 = 0.0761859..., gamma(5,10) = -(psi(1/2) + log(10))/10 is a generalized Euler constant, and gamma is Euler's constant (A001620) (Smith and Subbarao, 1981). - Amiram Eldar, Dec 30 2023
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| CROSSREFS
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Cf. A010879, A000005, A001227, A010879.
Cf. A001620, A002392, A020759 (psi(1/2)).
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| KEYWORD
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nonn,easy
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| STATUS
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approved
editing
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#8 by Alois P. Heinz at Wed Sep 11 12:10:00 EDT 2019
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#7 by Ilya Gutkovskiy at Wed Sep 11 12:09:04 EDT 2019
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#6 by Ilya Gutkovskiy at Wed Sep 11 12:01:43 EDT 2019
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