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A254318
Hyper equidigital numbers.
3
2, 3, 4, 5, 7, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 23, 24, 25, 28, 29, 31, 32, 35, 36, 37, 39, 41, 43, 46, 47, 49, 50, 53, 54, 58, 59, 61, 64, 67, 69, 71, 72, 73, 79, 81, 83, 89, 92, 93, 97, 98, 100, 101, 103, 104, 105, 106, 107, 109, 113, 116, 119
OFFSET
1,1
COMMENTS
The distinction between the equidigital numbers (A046758) is that only the distinct digits are counted instead of all digits. Hence the definition:
Write n as product of primes raised to powers, let D(n) = total number of distinct digits in product representation (number of distinct digits in all the primes and number of distinct digits in all the exponents that are greater than 1) and nbd(n) = A043537(n) = number of distinct digits in n; sequence gives n such that D(n) = nbd(n).
LINKS
EXAMPLE
116 is in the sequence because 116 = 2^2*29 => D(116)= A043537(116)=2.
MATHEMATICA
Cases[Range[400], n_ /; Length[Union[Flatten[IntegerDigits[FactorInteger[n] /. 1 -> Sequence[]]]]]==Length[Union[Flatten[IntegerDigits[n]]]]]
PROG
(PARI) for(n=1, 100, s=[]; F=factor(n); for(i=1, #F[, 1], s=concat(s, digits(F[i, 1])); if(F[i, 2]>1, s=concat(s, digits(F[i, 2])))); if(#vecsort(digits(n), , 8)==#vecsort(s, , 8), print1(n, ", "))) \\ Derek Orr, Jan 30 2015
KEYWORD
nonn,base
AUTHOR
Michel Lagneau, Jan 28 2015
STATUS
approved