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%I #22 Dec 10 2021 05:57:04
%S 0,1,3,6,10,15,16,18,21,25,30,36,38,41,45,50,56,63,66,70,75,81,88,96,
%T 100,105,111,118,126,135,140,146,153,161,170,180,181,183,186,190,195,
%U 201,203,206,210,215,221,228,231,235,240,246,253,261,265,270,276,283,291,300,305,311,318,326,335,345,351,358,366,375,385,396,398,401,405,410,416,423,426,430
%N a(n) = Sum_{i=0..n} digsum_6(i), where digsum_6(i) = A053827(i).
%D Jean-Paul Allouche and Jeffrey Shallit, Automatic sequences, Cambridge University Press, 2003, p. 94.
%H Vincenzo Librandi, <a href="/A231672/b231672.txt">Table of n, a(n) for n = 0..1000</a>
%H Jean Coquet, <a href="https://doi.org/10.1016/0022-314X(86)90067-3">Power sums of digital sums</a>, J. Number Theory, Vol. 22, No. 2 (1986), pp. 161-176.
%H P. J. Grabner, P. Kirschenhofer, H. Prodinger and R. F. Tichy, <a href="http://math.sun.ac.za/~hproding/abstract/abs_80.htm">On the moments of the sum-of-digits function</a>, <a href="http://math.sun.ac.za/~hproding/pdffiles/st_andrews.pdf">PDF</a>, Applications of Fibonacci numbers, Vol. 5 (St. Andrews, 1992), pp. 263-271, Kluwer Acad. Publ., Dordrecht, 1993.
%H Hsien-Kuei Hwang, Svante Janson and Tsung-Hsi Tsai, <a href="https://doi.org/10.1145/3127585">Exact and Asymptotic Solutions of a Divide-and-Conquer Recurrence Dividing at Half: Theory and Applications</a>, ACM Transactions on Algorithms, Vol. 13, No. 4 (2017), Article #47; <a href="https://www.researchgate.net/profile/Hsien-Kuei-Hwang/publication/320642171_Exact_and_Asymptotic_Solutions_of_a_Divide-and-Conquer_Recurrence_Dividing_at_Half_Theory_and_Applications/links/59f9a5be0f7e9b553ec0eaad">ResearchGate link</a>; <a href="http://140.109.74.92/hk/wp-content/files/2016/12/aat-hhrr-1.pdf">preprint</a>, 2016.
%H J.-L. Mauclaire and Leo Murata, <a href="https://dx.doi.org/10.3792/pjaa.59.274">On q-additive functions. I</a>, Proc. Japan Acad. Ser. A Math. Sci., Vol. 59, No. 6 (1983), pp. 274-276.
%H J.-L. Mauclaire and Leo Murata, <a href="https://dx.doi.org/10.3792/pjaa.59.441">On q-additive functions. II</a>, Proc. Japan Acad. Ser. A Math. Sci., Vol. 59, No. 9 (1983), pp. 441-444.
%H J. R. Trollope, <a href="http://www.jstor.org/stable/2687954">An explicit expression for binary digital sums</a>, Math. Mag., Vol. 41, No. 1 (1968), pp. 21-25.
%F a(n) ~ 5*n*log(n)/(2*log(6)). - _Amiram Eldar_, Dec 09 2021
%t Accumulate[f[n_]:=n - 5 Sum[Floor[n/6^k], {k, n}]; Array[f, 100, 0]] (* _Vincenzo Librandi_, Sep 04 2016 *)
%o (PARI) a(n) = sum(i=0, n, sumdigits(i, 6)); \\ _Michel Marcus_, Dec 09 2021
%Y Cf. A053827, A231673, A231674, A231675.
%K nonn,base
%O 0,3
%A _N. J. A. Sloane_, Nov 13 2013