A287894 Sum of the digit sums of the n-th powers of the first n positive integers.

1, 5, 18, 30, 33, 94, 136, 186, 225, 268, 348, 413, 502, 682, 792, 938, 1098, 1254, 1441, 1529, 1647, 1905, 2148, 2392, 2674, 2961, 3150, 3493, 3804, 4007, 4417, 4636, 5103, 5576, 5850, 6234, 6769, 7175, 7659, 7713, 8538, 8848, 9406, 9957, 10332, 11218, 11877

Offset: 1

Author

Marian Kraus, Jun 02 2017

Keywords

• nonn
• base

Comments

The sequence is not increasing: a(100) < a(99). - Robert Israel, Jun 30 2017

Examples

			n=1: 1: 1;
n=2: 1,4: 1+4=5;
n=3: 1,8,27: 1+8+9=18;
n=4: 1,16,81,256: 1+7+9+13=30.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A007953.

Programs

Maple

ds:= n -> convert(convert(n,base,10),`+`):
f:= n -> add(ds(k^n),k=1..n):
map(f, [$1..50]); # Robert Israel, Jun 30 2017

Mathematica

a[n_] := Sum[ Total@ IntegerDigits[k^n], {k, n}]; Array[a, 50] (* Giovanni Resta, Jun 07 2017 *)

PARI

a(n) = sum(k=1, n, sumdigits(k^n)); \\ Michel Marcus, Jun 06 2017

Formula

a(n) = Sum_{k=1..n} digsum(k^n), n >= 1.