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%I #26 Nov 12 2022 06:20:51
%S 20345,23405,30245,30425,32045,40235,40325,42035,43025,45050,45450,
%T 50450,52023,22043435,22053335,23234545,23344501,23452345,24034455,
%U 24243535,24352435,24403451,24433051,30034454,30202455,30334045,30340454,30424235
%N Integers k such that in the list of divisors of k (in base 6), each digit 0-5 appears equally often.
%H Naohiro Nomoto, <a href="https://web.archive.org/web/20000916012426/http://www.geocities.co.jp/Technopolis/1793/09digit.htm">In the list of divisors of n,... </a>
%e Divisors of 45050 are (1,2,3,10,4505,13414,22323,45050); the numbers of digits (0-5) are [ 0(4),1(4),2(4),3(4),4(4),5(4) ]
%p k := 0:for i from 1 to 35000 do for j from 0 to 5 do a[j] := 0:end do:c := divisors(i):for j from 1 to nops(c) do b := convert(c[j],base,6); for h from 1 to nops(b) do a[ b[h] ] := a[ b[h] ]+1:end do:end do: if(a[0]=a[1] and a[1]=a[2] and a[2]=a[3] and a[4]=a[5]) then k := k+1:q := convert(i,base,6):d[k] := sum(q[o+1]*10^o,o=0..nops(q)-1):end if:end do: q := seq(d[l],l=1..k);
%p isA045815 := proc(n) local c,j,b,h,a,q ; a := [0,0,0,0,0,0] : c := numtheory[divisors](n): for j from 1 to nops(c) do b := convert(c[j], base, 6); for h from 1 to nops(b) do a[b[h]+1] := a[b[h]+1]+1: end do: end do: if(a[1]=a[2] and a[2]=a[3] and a[3]=a[4] and a[4]=a[5] and a[5]=a[6]) then q := convert(n,base,6) ; add(q[o+1]*10^o,o=0..nops(q)-1) ; else -1 ; end if: end: n := 1: while true do a := isA045815(n) : if a >= 0 then printf("%d, ",a) ; fi ; n := n+1 : od : # _R. J. Mathar_, Jun 26 2007
%Y Cf. A038564, A038565, A045816.
%K easy,nonn,base
%O 1,1
%A _Naohiro Nomoto_
%E More terms from _Sascha Kurz_, Mar 24 2002
%E Corrected by _R. J. Mathar_, Jun 26 2007
%E More terms from _Sean A. Irvine_, Sep 26 2011
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