A254318 Hyper equidigital numbers.

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

Michel Lagneau, Table of n, a(n) for n = 1..10000

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

Crossrefs

Cf. A043537, A046760, A046758, A046759, A254315, A254317, A254319, A254321.

Sequence in context: A214652 A137929 A094617 * A047502 A356311 A117092

Adjacent sequences: A254315 A254316 A254317 * A254319 A254320 A254321

Keyword

nonn,base

Author

Michel Lagneau, Jan 28 2015

Status

approved