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

1,1

Links

Table of n, a(n) for n=1..28.

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

Example

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) ]

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

Crossrefs

Cf. A038564, A038565, A045816.

Sequence in context: A234631 A343243 A156408 * A182294 A103912 A256104

Adjacent sequences: A045812 A045813 A045814 * A045816 A045817 A045818

Keyword

easy,nonn,base

Author

Naohiro Nomoto

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

Status

approved