A231688 a(n) = Sum_{i=0..n} digsum(i)^3, where digsum(i) = A007953(i).

0, 1, 9, 36, 100, 225, 441, 784, 1296, 2025, 2026, 2034, 2061, 2125, 2250, 2466, 2809, 3321, 4050, 5050, 5058, 5085, 5149, 5274, 5490, 5833, 6345, 7074, 8074, 9405, 9432, 9496, 9621, 9837, 10180, 10692, 11421, 12421, 13752, 15480, 15544, 15669, 15885, 16228, 16740, 17469, 18469, 19800, 21528, 23725, 23850, 24066, 24409, 24921, 25650, 26650, 27981, 29709, 31906, 34650

Offset: 0

Author

N. J. A. Sloane, Nov 13 2013

Keywords

• nonn
• base

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

• Indranil Ghosh, Table of n, a(n) for n = 0..10000
• J. Coquet, Power sums of digital sums, J. Number Theory 22 (1986), no. 2, 161-176.
• R. E. Kennedy and C. N. Cooper, An extension of a theorem by Cheo and Yien concerning digital sums, Fibonacci Q. 29, No. 2, 145-149 (1991).
• 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.
• H. Riede, Asymptotic estimation of a sum of digits, Fibonacci Q. 36, No. 1, 72-75 (1998).
• J. R. Trollope, An explicit expression for binary digital sums, Math. Mag. 41 1968 21-25.

Crossrefs

Cf. A007953, A037123, A074784, A231689.

Partial sums of A118880.

Programs

Maple

See A037123.

Mathematica

Accumulate[Table[Total[IntegerDigits[n]]^3,{n,0,60}]] (* Harvey P. Dale, Aug 06 2021 *)

PARI

a(n) = sum(i=0, n, sumdigits(i)^3); \\ Michel Marcus, Jan 07 2017