A231686 a(n) = Sum_{i=0..n} digsum_9(i)^3, where digsum_9(i) = A053830(i).

0, 1, 9, 36, 100, 225, 441, 784, 1296, 1297, 1305, 1332, 1396, 1521, 1737, 2080, 2592, 3321, 3329, 3356, 3420, 3545, 3761, 4104, 4616, 5345, 6345, 6372, 6436, 6561, 6777, 7120, 7632, 8361, 9361, 10692, 10756, 10881, 11097, 11440, 11952, 12681, 13681, 15012, 16740, 16865, 17081, 17424, 17936, 18665, 19665, 20996, 22724, 24921, 25137, 25480, 25992, 26721, 27721, 29052

Offset: 0

Author

N. J. A. Sloane, Nov 13 2013

Keywords

• nonn
• base

Links

• Jean Coquet, Power sums of digital sums, J. Number Theory 22 (1986), no. 2, 161-176.
• P. J. Grabner, P. Kirschenhofer, H. Prodinger, R. F. Tichy, On the moments of the sum-of-digits function, PDF, Applications of Fibonacci numbers, Vol. 5 (St. Andrews, 1992), 263-271, Kluwer Acad. Publ., Dordrecht, 1993.
• J.-L. Mauclaire, Leo Murata, On q-additive functions. I, Proc. Japan Acad. Ser. A Math. Sci. 59 (1983), no. 6, 274-276.
• J.-L. Mauclaire, 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.

Crossrefs

Cf. A053830, A231684, A231685, A231687.

Programs

Mathematica

Accumulate[Table[Total[IntegerDigits[n,9]]^3,{n,0,60}]] (* Harvey P. Dale, Dec 22 2020 *)

PARI

a(n) = sum(i=0, n, sumdigits(i, 9)^3); \\ Michel Marcus, Sep 20 2017