%I #46 Sep 08 2022 08:45:04
%S 1,1,2,3,4,5,6,8,9,11,12,13,15,17,18,20,21,23,25,27,28,30,32,34,35,37,
%T 39,41,43,45,47,49,51,53,55,57,59,61,63,65,67,69,71,73,75,77,79,81,83,
%U 85,88,90,92,94,96,98,101,103,105,107,109,112,114,116,118,121,123,125
%N Number of digits in n^n.
%C This is almost certainly the same as the number of decimal digits of the sum of the n-th powers of the divisors of n (a sequence submitted by _Labos Elemer_ on Jan 14 2002). Although no formal proof for this is known, _Jon E. Schoenfield_ has verified it for n up to 10^8 and has given a plausible heuristic argument that it is true for all n.
%H Harry J. Smith, <a href="/A066022/b066022.txt">Table of n, a(n) for n=1..1000</a>
%F a(n) = A055642(A000312(n)). - _Michel Marcus_, Dec 05 2019
%p [seq(length(n^n), n=1..55)]; # _Zerinvary Lajos_, Mar 10 2007
%t Table[IntegerLength[n^n], {n, 80}] (* _Vincenzo Librandi_, Mar 08 2015 *)
%o (PARI) a(n)=#digits(n^n); \\ _Joerg Arndt_, Apr 30 2020
%o (Magma) [ #Intseq(n^n): n in [1..80] ]; // _Vincenzo Librandi_, Mar 08 2015
%Y Cf. A000312, A054382, A055642.
%K base,easy,nonn
%O 1,3
%A Robert A. Stump (bee_ess107(AT)yahoo.com), Dec 11 2001
%E Edited by _N. J. A. Sloane_ Jan 03 2009 at the suggestion of _Jon E. Schoenfield_.