This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A342108 #22 May 07 2025 12:36:02
%S A342108 2,10,102,1110,10010,101010,1009470,11741730,223092870,6469693230
%N A342108 Smallest positive integer m with n digits and such that omega(m) = bigomega(m) = n.
%C A342108 Equivalently: smallest n-digit squarefree number with n distinct prime factors.
%C A342108 Differs from A036336 where length(m) = bigomega(m) = n, when length(m) is the number of digits of m (A055642) and the n prime factors of m are counted with multiplicity (A001222).
%C A342108 Differs from A070842 where length(m) = omega(m) = n, when length(m) is the number of digits of m (A055642) and omega(m) is the number of distinct prime factors dividing m (A001221).
%C A342108 The first index for which these three sequences give three distinct terms is 4:
%C A342108 -> a(4) = 1110 = 2 * 3 * 5 * 37 , with length(1110) = omega(1110) = bigomega(1110) = 4.
%C A342108 -> A036336(4) = 1012 = 2 * 2 * 11 * 23 with length(1012) = bigomega(1012) = 4 > omega(1012) = 3.
%C A342108 -> A070842(4) = 1020 = 2 * 2 * 3 * 5 * 17 with length(1020) = omega(1020) = 4 < bigomega(1020) = 5.
%C A342108 As these terms are the smallest n-digit numbers in A167050 that is finite, this sequence is also finite with 10 terms, as for A070842.
%F A342108 A036336(n) <= A070842(n) <= a(n).
%e A342108 10010 = 2*5*7*11*13 is the smallest 5-digit number such that omega(10010) = bigomega(10010) = 5, hence a(5) = 10010.
%t A342108 a={};For[n=1,n<=10,n++,For[m=10^(n-1),m<10^n,m++,If[PrimeOmega[m]==PrimeNu[m]==n,AppendTo[a,m];Break[]]]];a (* _Stefano Spezia_, Mar 04 2021 *)
%Y A342108 Subsequence of A167050.
%Y A342108 Cf. A001221, A001222, A055642.
%Y A342108 Cf. A036336, A070842, A342109.
%K A342108 nonn,fini,full,base
%O A342108 1,1
%A A342108 _Bernard Schott_, Feb 28 2021