A231689 a(n) = Sum_{i=0..n} digsum(i)^4, where digsum(i) = A007953(i).

0, 1, 17, 98, 354, 979, 2275, 4676, 8772, 15333, 15334, 15350, 15431, 15687, 16312, 17608, 20009, 24105, 30666, 40666, 40682, 40763, 41019, 41644, 42940, 45341, 49437, 55998, 65998, 80639, 80720, 80976, 81601, 82897, 85298, 89394, 95955, 105955, 120596, 141332, 141588, 142213, 143509, 145910, 150006, 156567, 166567, 181208, 201944, 230505, 231130, 232426, 234827, 238923

Offset: 0

Author

N. J. A. Sloane, Nov 13 2013

Keywords

• nonn
• base

Links

• Amiram Eldar, Table of n, a(n) for n = 0..10001
• Jean Coquet, Power sums of digital sums, J. Number Theory, Vol. 22, No. 2 (1986), pp. 161-176.
• P. J. Grabner, P. Kirschenhofer, H. Prodinger and R. F. Tichy, On the moments of the sum-of-digits function, PDF, Applications of Fibonacci numbers, Vol. 5 (St. Andrews, 1992), Kluwer Acad. Publ., Dordrecht, 1993, pp. 263-271.
• Robert E. Kennedy and Curtis N. Cooper, An extension of a theorem by Cheo and Yien concerning digital sums, Fibonacci Quarterly, Vol. 29, No. 2 (1991), pp. 145-149.
• J.-L. Mauclaire and Leo Murata, On q-additive functions. I, Proc. Japan Acad. Ser. A Math. Sci., Vol. 59, No. 6 (1983), pp. 274-276.
• J.-L. Mauclaire and Leo Murata, On q-additive functions. II, Proc. Japan Acad. Ser. A Math. Sci., Vol. 59, No. 9 (1983), pp. 441-444.
• Harald Riede, Asymptotic estimation of a sum of digits, Fibonacci Quarterly, Vol. 36, No. 1 (1998), pp. 72-75.
• J. R. Trollope, An explicit expression for binary digital sums, Math. Mag., Vol. 41, No. 1 (1968), pp. 21-25.

Crossrefs

Cf. A007953, A037123, A074784, A231688.

Programs

Maple

See A037123.

Mathematica

Accumulate[Table[Total[IntegerDigits[n]]^4,{n,0,60}]] (* Harvey P. Dale, May 12 2014 *)

PARI

a(n) = sum(i=0, n, sumdigits(i)^4); \\ Michel Marcus, Sep 20 2017