A307764 Numbers m whose distinct prime factors are exactly the same as the distinct prime factors of each of the numbers obtained by deleting any single digit in the decimal expansion of m.

2500, 3600, 9600, 25000, 36000, 96000, 250000, 360000, 960000, 2500000, 3600000, 9600000, 25000000, 36000000, 96000000, 250000000, 360000000, 960000000, 2500000000, 3600000000, 9600000000, 25000000000, 36000000000, 96000000000, 250000000000, 360000000000

Offset

1,1

Comments

Conjecture: a(3n-2) = 25*10^(n+1), a(3n-1) = 36*10^(n+1) and a(3n) = 96*10^(n+1).

Links

Table of n, a(n) for n=1..26.

Example

3600 is in the sequence because 3600, 360, 600 and 300 contain all the same prime factors 2, 3 and 5.

Maple

with(numtheory):nn:=10^10:
for n from 100 to nn do:
it:=0:x:=convert(n, base, 10):n0:=nops(x):d:=factorset(n):
W:=array(1..n0-1):
  for i from 1 to n0 do :
   k:=0:
   for j from n0 by -1 to 1 do:
    if j<>i
     then
     k:=k+1: W[k]:=x[j]:
     else
    fi:
   od:
    s:=sum(‘W[i]*10^(n0-i-1)’, ‘i’=1..n0-1):d1:=factorset(s):
      if d=d1
       then
       it:=it+1:
       else
      fi:
   od:
    if it=n0
     then
     printf(`%d, `, n):
     else
    fi:
od:

Mathematica

rad[0] = 0; rad[n_] := Times @@ (First@# & /@ FactorInteger[n]); Select[Range[ 10^6], {rad[#]} == Union[rad /@ (FromDigits/@Subsets[(d = IntegerDigits[#]), {Length[d] - 1}])] &] (* Amiram Eldar, Jul 26 2019 *)

Crossrefs

Cf. A027748.

Sequence in context: A248548 A252315 A131523 * A062120 A220025 A253377

Adjacent sequences: A307761 A307762 A307763 * A307765 A307766 A307767

Keyword

nonn,base

Author

Michel Lagneau, Jul 24 2019

Status

approved