A045817 - OEIS

%I #16 Sep 08 2018 04:22:53

%S 3602,246506,264533,266405,303652,320556,324255,325605,342560,345064,

%T 345406,345604,346340,362055,414056,430462,434630,435065,436430,

%U 436550,453605,500426,500641,506022,524360,524406,526433,530632,532650,533402

%N Numbers n written in base 7, where in the list of divisors of n (in base 7), each digit 0-6 appears equally often.

%H Robert Israel, <a href="/A045817/b045817.txt">Table of n, a(n) for n = 1..161</a>

%H N. Nomoto, <a href="http://www.geocities.co.jp/Technopolis/1793/09digit.htm">In the list of divisors of n,... </a> [broken link]

%e E.g., divisors of 342560 (base 7) are (1,2,10,20,15463,34256,154630,342560) (all in base 7); the numbers of digits (0-6) are [0(4),1(4),2(4),3(4),4(4),5(4),6(4)].

%p N:= 7^6:

%p cv7:= proc(n) local L; L:= convert(n,base,7);

%p add(L[i]*10^(i-1),i=1..nops(L)) end proc:

%p V:= Matrix(N,7,datatype=integer[8]):

%p count:= 0: Res:= NULL:

%p for i from 1 to N do

%p   L:= convert(i,base,7);

%p   M:= Vector[row]([seq(numboccur(d,L),d=0..6)],datatype=integer[8]);

%p   for r from i to N by i do V[r,..]:= V[r,..] + M od;

%p   if nops(convert(V[i,..],set))=1 then

%p     count:= count+1;

%p     w:= cv7(i);

%p     Res:= Res,w;

%p   fi

%p od:

%p Res; # _Robert Israel_, Sep 07 2018

%Y Cf. A038564, A038565, A045818.

%K easy,nonn,base

%O 1,1

%A _Naohiro Nomoto_

%E Definition clarified by _Robert Israel_, Sep 07 2018