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A045815
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Integers k such that in the list of divisors of k (in base 6), each digit 0-5 appears equally often.
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1
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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
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OFFSET
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1,1
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LINKS
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EXAMPLE
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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) ]
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MAPLE
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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
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CROSSREFS
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KEYWORD
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easy,nonn,base
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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