A218442 a(n) = Sum_{k=0..n} floor(n/(3*k + 1)).
0, 1, 2, 3, 5, 6, 7, 9, 11, 12, 14, 15, 17, 19, 21, 22, 25, 26, 27, 29, 32, 34, 36, 37, 39, 41, 43, 44, 48, 49, 51, 53, 56, 57, 59, 61, 63, 65, 67, 69, 73, 74, 76, 78, 81, 82, 84, 85, 88, 91, 94, 95, 99, 100, 101, 103, 107, 109, 111, 112, 115, 117, 119, 121, 125, 127, 129, 131, 134, 135, 139, 140, 142, 144, 146, 148, 152
Offset: 0
Links
- Amiram Eldar, Table of n, a(n) for n = 0..10000
- R. A. Smith and M. V. Subbarao, The average number of divisors in an arithmetic progression, Canadian Mathematical Bulletin, Vol. 24, No. 1 (1981), pp. 37-41.
Programs
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Mathematica
d[n_] := DivisorSum[n, 1 &, Mod[#, 3] == 1 &]; d[0] = 0; Accumulate@Array[d, 100, 0] (* Amiram Eldar, Nov 25 2023 *)
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Maxima
A218442[n]:=sum(floor(n/(3*k+1)),k,0,n)$ makelist(A218442[n],n,0,80); /* Martin Ettl, Oct 29 2012 */
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PARI
a(n)=sum(k=0,n\3,(n\(3*k+1)))
Formula
a(n) = n*log(n)/3 + c*n + O(n^(1/3)*log(n)), where c = gamma(1,3) - (1 - gamma)/3 = A256425 - (1 - A001620)/3 = 0.536879... (Smith and Subbarao, 1981). - Amiram Eldar, Nov 25 2023