%I
%S 2500,3600,9600,25000,36000,96000,250000,360000,960000,2500000,
%T 3600000,9600000,25000000,36000000,96000000,250000000,360000000,
%U 960000000,2500000000,3600000000,9600000000,25000000000,36000000000,96000000000,250000000000,360000000000
%N 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.
%C Conjecture: a(3n2) = 25*10^(n+1), a(3n1) = 36*10^(n+1) and a(3n) = 96*10^(n+1).
%e 3600 is in the sequence because 3600, 360, 600 and 300 contain all the same prime factors 2, 3 and 5.
%p with(numtheory):nn:=10^10:
%p for n from 100 to nn do:
%p it:=0:x:=convert(n,base,10):n0:=nops(x):d:=factorset(n):
%p W:=array(1..n01):
%p for i from 1 to n0 do :
%p k:=0:
%p for j from n0 by 1 to 1 do:
%p if j<>i
%p then
%p k:=k+1: W[k]:=x[j]:
%p else
%p fi:
%p od:
%p s:=sum(āW[i]*10^(n0i1)ā, āiā=1..n01):d1:=factorset(s):
%p if d=d1
%p then
%p it:=it+1:
%p else
%p fi:
%p od:
%p if it=n0
%p then
%p printf(`%d, `,n):
%p else
%p fi:
%p od:
%t 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 *)
%Y Cf. A027748.
%K nonn,base
%O 1,1
%A _Michel Lagneau_, Jul 24 2019
