This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A381487 #26 Feb 27 2025 07:12:07
%S A381487 0,1,2,3,4,5,6,7,8,9,81,128,256,512,729,2401,6561,8192,16384,32768,
%T A381487 59049,78125,524288,531441,823543,1048576,2097152,4782969,33554432,
%U A381487 43046721,67108864,134217728,282475249,387420489,1220703125,2147483648,3486784401,4294967296
%N A381487 Numbers which are a power of their digital root.
%H A381487 Michel Marcus, <a href="/A381487/b381487.txt">Table of n, a(n) for n = 1..3347</a>
%F A381487 a(n) = A381491(n)^A381492(n).
%e A381487 a(12) = 128 is a term since 128 = 2^7 = A010888(128)^7.
%t A381487 A010888[n_]:=n - 9*Floor[(n-1)/9]; kmax=5*10^6; a={0,1}; For[k=2, k<=kmax, k++, If[A010888[k]!=1, If[IntegerQ[Log[A010888[k],k]], AppendTo[a,k]]]]; a
%o A381487 (PARI) isok(k) = if ((k==0) || (k==1), return(1)); my(d=(k-1)%9+1); if (d>1, d^logint(k, d) == k); \\ _Michel Marcus_, Feb 26 2025
%o A381487 (PARI) lista(nn) = my(list = List()); listput(list, 0); listput(list, 1); for (n=2, 9, for (k=1, logint(nn, n), if ((n^k-1)%9+1 == n, listput(list, n^k)););); vecsort(Vec(list)); \\ _Michel Marcus_, Feb 27 2025
%Y A381487 Cf. A010888, A023106, A381491, A381492.
%Y A381487 Digital root of k^n: A000012 (1), A153130 (2), A100401 (3), A100402 (4), A070366 (5), A100403 (6), A070403 (7), A010689 (8), A010734 (9).
%K A381487 nonn,base
%O A381487 1,3
%A A381487 _Stefano Spezia_, Feb 25 2025