A045815 Integers k such that in the list of divisors of k (in base 6), each digit 0-5 appears equally often.

20345, 23405, 30245, 30425, 32045, 40235, 40325, 42035, 43025, 45050, 45450, 50450, 52023, 22043435, 22053335, 23234545, 23344501, 23452345, 24034455, 24243535, 24352435, 24403451, 24433051, 30034454, 30202455, 30334045, 30340454, 30424235

Offset: 1

Author

Naohiro Nomoto

Keywords

• easy
• nonn
• base

Examples

			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) ]
		

Links

• Naohiro Nomoto, In the list of divisors of n,...

Crossrefs

Cf. A038564, A038565, A045816.

Programs

Maple

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);
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

Extensions

More terms from Sascha Kurz, Mar 24 2002

Corrected by R. J. Mathar, Jun 26 2007

More terms from Sean A. Irvine, Sep 26 2011