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

1,2

Comments

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

Links

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

Formula

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

Example

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.

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 *)

Prog

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

Crossrefs

Cf. A007953.

Sequence in context: A034108 A155450 A322409 * A140365 A063294 A063141

Adjacent sequences: A287891 A287892 A287893 * A287895 A287896 A287897

Keyword

nonn,base

Author

Marian Kraus, Jun 02 2017

Status

approved