A087331 -id:A087331 - cp's OEIS frontend

A087450 Smallest number (see comment for representation) with all identical digits having n distinct prime divisors.

11, 12, 16, 26, 46, 61, 62, 121, 122, 182, 241, 242, 322, 301, 302, 422, 642, 646, 722, 1006, 601, 602, 842, 962, 1261, 1262, 1201, 1202, 2042, 1681, 1682, 1922, 1801, 1802, 2102, 2402, 2522, 3302, 3361, 3362, 3001, 3002

Offset: 1

Robert G. Wilson v, Sep 06 2003

Sequence represented by citing the number of repeated digits concatenated with that digit, i.e. a(8) = 122.

No more terms < 3600. - David Wasserman, Jun 03 2005

			a(6) = 86 because 66666666= 2*3*11*73*101*137, is 8 digits long and has 6 distinct prime divisors.

Cf. A087331.

PrimeFactors[n_Integer] := Flatten[Table[ #[[1]], {1}] & /@ FactorInteger[n]]; Do[k = 1; While[t = Table[j*(10^k - 1)/9, {j, 1, 9}]; l = Map[Length, Map[PrimeFactors, t]]; Position[l, n] == {}, k++ ]; d = t[[Position[l, n][[1, 1]]]]; Print[10k + Position[l, n][[1, 1]]], {n, 0, 17}]

More terms from David Wasserman, Jun 03 2005

A268582 Sphenic numbers having identical digits.

Original entry on oeis.org

66, 222, 555, 777, 2222, 3333, 5555, 7777, 22222, 33333, 55555, 77777, 2222222, 3333333, 5555555, 7777777, 22222222222, 33333333333, 55555555555, 77777777777, 1111111111111, 22222222222222222, 33333333333333333, 55555555555555555, 77777777777777777, 6666666666666666666

Offset: 1

Michel Lagneau, Feb 07 2016

Subsequence of A007304 (sphenic numbers: products of 3 distinct primes).

a(1)= A087331(4).

			222 is in the sequence because 222 = 2*3*37, product of 3 distinct primes.

Max Alekseyev, Table of n, a(n) for n = 1..89

Cf. A007304, A046053, A087331, A095370, A196104.

with(numtheory):
for n from 1 to 23 do:
  for b from 1 to 9 do:
    x:=(((10^n)- 1)/9)*b:y:=factorset(x):n1:=nops(y):
     if bigomega(x)=3 and n1=3
      then
      printf(`%d, `,x):
      else
     fi:
   od:
od:

Select[Flatten@ Map[Map[Function[k, FromDigits@ Table[k, {#}]], Range[1, 9]] &, Range@ 20], Length@ # == 3 && Times @@ Last /@ # == 1 &@ FactorInteger@ # &] (* Michael De Vlieger, Feb 07 2016 *)

A199166 Smallest number with all identical digits having n prime factors with multiplicity.

Original entry on oeis.org

2, 4, 8, 88, 888, 222222, 444444, 888888, 444444444444, 888888888888, 444444444444444444, 888888888888888888, 888888888888888888888888, 222222222222222222222222222222, 444444444444444444444444444444, 888888888888888888888888888888

Offset: 1

Michel Lagneau, Nov 03 2011

			a(7) = 444444 = 2^2*3*7*11*13*37 has 7 prime factors with multiplicity, hence 444444 is in the sequence.

Cf. A087331.

with(numtheory):for n from 1 to 17 do:i:=0:for k from 1 to 60 while(i=0)do:for a from 1 to 9 while(i=0)do:x:=((10^k- 1)/9)*a:if bigomega(x)=n then i:=1:printf(`%d, `,x):else fi:od:od:od:

Table[digs = 1; While[i = 1; While[num = FromDigits[Table[i, {digs}]]; stop = (i > 9) || PrimeOmega[num] == n; ! stop, i++]; i > 9, digs++]; num, {n, 16}] (* T. D. Noe, Nov 03 2011 *)

min{ A010785(k): A001222(A010785(k)) = n}. - R. J. Mathar, Nov 03 2011

cp's OEIS Frontend

A087450 Smallest number (see comment for representation) with all identical digits having n distinct prime divisors.

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

Mathematica

Extensions

A268582 Sphenic numbers having identical digits.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Maple

Mathematica

A199166 Smallest number with all identical digits having n prime factors with multiplicity.

Views

Author

Keywords

Examples

Crossrefs

Programs

Maple

Mathematica

Formula