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

%I A287894 #21 Jun 30 2017 20:38:50
%S A287894 1,5,18,30,33,94,136,186,225,268,348,413,502,682,792,938,1098,1254,
%T A287894 1441,1529,1647,1905,2148,2392,2674,2961,3150,3493,3804,4007,4417,
%U A287894 4636,5103,5576,5850,6234,6769,7175,7659,7713,8538,8848,9406,9957,10332,11218,11877
%N A287894 Sum of the digit sums of the n-th powers of the first n positive integers.
%C A287894 The sequence is not increasing: a(100) < a(99). - _Robert Israel_, Jun 30 2017
%H A287894 Robert Israel, <a href="/A287894/b287894.txt">Table of n, a(n) for n = 1..1000</a>
%F A287894 a(n) = Sum_{k=1..n} digsum(k^n), n >= 1.
%e A287894 n=1: 1: 1;
%e A287894 n=2: 1,4: 1+4=5;
%e A287894 n=3: 1,8,27: 1+8+9=18;
%e A287894 n=4: 1,16,81,256: 1+7+9+13=30.
%p A287894 ds:= n -> convert(convert(n,base,10),`+`):
%p A287894 f:= n -> add(ds(k^n),k=1..n):
%p A287894 map(f, [$1..50]); # _Robert Israel_, Jun 30 2017
%t A287894 a[n_] := Sum[ Total@ IntegerDigits[k^n], {k, n}]; Array[a, 50] (* _Giovanni Resta_, Jun 07 2017 *)
%o A287894 (PARI) a(n) = sum(k=1, n, sumdigits(k^n)); \\ _Michel Marcus_, Jun 06 2017
%Y A287894 Cf. A007953.
%K A287894 nonn,base
%O A287894 1,2
%A A287894 _Marian Kraus_, Jun 02 2017