A288157 Number of bases b < n where the digits of n are not all different.
0, 0, 1, 2, 2, 2, 2, 3, 3, 4, 2, 4, 3, 4, 3, 5, 4, 5, 2, 5, 4, 5, 4, 6, 5, 6, 4, 5, 4, 6, 5, 7, 5, 6, 4, 8, 6, 5, 4, 7, 5, 7, 6, 6, 6, 7, 5, 8, 6, 8, 5, 6, 4, 6, 6, 7, 7, 6, 5, 11, 7, 7, 7, 10, 7, 7, 6, 7, 5, 7, 6, 11, 6, 8, 7, 7, 6, 9, 6, 9, 9, 7, 5, 10, 7, 6, 7, 9, 7, 10, 8, 10, 8, 7, 6, 10, 7, 10, 6
Offset: 1
Examples
a(10)=4 because 10 equals 1010 base 2 (repeating both 0 and 1), 101 base 3 (repeating 1), 22 base 4 (repeating 2) and 11 base 9 (repeating 1), and 20, 14, 13, 12 in the other bases < 10, not repeating digits.
Links
- Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
Crossrefs
a(n) = n - 1 - A270832(n).
Programs
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Mathematica
Table[n - 1 - Boole[n > 1] - Count[Range[2, n - 1], b_ /; UnsameQ @@ IntegerDigits[n, b]], {n, 99}] (* Michael De Vlieger, Jun 15 2017 *) -
PARI
a(n) = sum(b=2, n, d = digits(n, b); #d != #Set(d)); \\ Michel Marcus, Jun 13 2017
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PARI
a(n)=my(s=sqrtint(n)); sum(b=2, s, my(d=digits(n,b)); #Set(d)!=#d) + sum(k=1,n\(s+1), n%k==0 && n/k>s+1) \\ Charles R Greathouse IV, Jun 15 2017