A254319 Hyper economical numbers.

27, 108, 125, 128, 129, 135, 138, 143, 159, 160, 184, 187, 189, 196, 207, 209, 216, 219, 243, 249, 256, 259, 265, 276, 295, 297, 329, 341, 351, 375, 403, 429, 451, 458, 469, 497, 512, 529, 621, 625, 671, 679, 729, 781, 795, 837, 841, 892, 896, 908, 916, 932

Offset

1,1

Comments

The distinction between the economical numbers (A046759) is that the distinct digits are counted only instead 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

Table of n, a(n) for n=1..52.

Example

27 is in the sequence because 27 = 3 ^ 3 => D(27)= 1 < nbd(27)=2.

Mathematica

Cases[Range[400], n_ /; Length[Union[Flatten[IntegerDigits[FactorInteger[n] /. 1 -> Sequence[]]]]]< Length[Union[Flatten[IntegerDigits[n]]]]]

Prog

(PARI) for(n=1, 10^3, 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, A254318, A254321.

Sequence in context: A140376 A046347 A158549 * A044278 A044659 A244634

Adjacent sequences: A254316 A254317 A254318 * A254320 A254321 A254322

Keyword

nonn,base

Author

Michel Lagneau, Jan 28 2015

Status

approved