A231674 a(n) = Sum_{i=0..n} digsum_6(i)^3, where digsum_6(i) = A053827(i).

0, 1, 9, 36, 100, 225, 226, 234, 261, 325, 450, 666, 674, 701, 765, 890, 1106, 1449, 1476, 1540, 1665, 1881, 2224, 2736, 2800, 2925, 3141, 3484, 3996, 4725, 4850, 5066, 5409, 5921, 6650, 7650, 7651, 7659, 7686, 7750, 7875, 8091, 8099, 8126, 8190, 8315, 8531, 8874, 8901, 8965, 9090, 9306, 9649, 10161, 10225, 10350, 10566, 10909, 11421, 12150, 12275, 12491, 12834, 13346

Offset

0,3

References

Grabner, P. J.; Kirschenhofer, P.; Prodinger, H.; Tichy, R. F.; On the moments of the sum-of-digits function. Applications of Fibonacci numbers, Vol. 5 (St. Andrews, 1992), 263-271, Kluwer Acad. Publ., Dordrecht, 1993.

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

J. Coquet, Power sums of digital sums, J. Number Theory 22 (1986), no. 2, 161-176.

J.-L. Mauclaire and Leo Murata, On q-additive functions, I. Proc. Japan Acad. Ser. A Math. Sci. 59 (1983), no. 6, 274-276.

J.-L. Mauclaire and Leo Murata, On q-additive functions, II. Proc. Japan Acad. Ser. A Math. Sci. 59 (1983), no. 9, 441-444.

J. R. Trollope, An explicit expression for binary digital sums, Math. Mag. 41 1968 21-25.

Mathematica

Accumulate[f[n_]:=n - 5Sum[Floor[n/6^k], {k, n}]; Array[f, 100, 0]^3] (* Vincenzo Librandi, Sep 04 2016 *)

Crossrefs

Cf. A053827, A231672, A231673, A231675.

Sequence in context: A134537 A066647 A187607 * A085037 A231678 A231682

Adjacent sequences: A231671 A231672 A231673 * A231675 A231676 A231677

Keyword

nonn,base

Author

N. J. A. Sloane, Nov 13 2013

Status

approved