A254318 -id:A254318 - cp's OEIS frontend

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

Michel Lagneau, Jan 28 2015

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).

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

Cf. A043537, A046760, A046758, A046759, A254318, A254321.

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

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

A254321 Hyper Wasteful numbers.

Original entry on oeis.org

6, 8, 9, 22, 26, 30, 33, 34, 38, 40, 42, 44, 45, 48, 51, 52, 55, 56, 57, 60, 62, 63, 65, 66, 68, 70, 74, 75, 76, 77, 78, 80, 82, 84, 85, 86, 87, 88, 90, 91, 94, 95, 96, 99, 102, 110, 111, 112, 114, 115, 117, 118, 122, 130, 133, 136, 141, 144, 152, 153, 155, 161

Offset: 1

Michel Lagneau, Jan 28 2015

The distinction between the Wasteful numbers (A046760) 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).

			88 is in the sequence because 88 = 2 ^ 3 * 11 => D(88)=3 > nbd(88)=1.

Cf. A043537, A046760, A046758, A046759, A254318, A254319.

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

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

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A254319 Hyper economical numbers.

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