cp's OEIS Frontend

A342109 Largest positive integer m with n digits and such that omega(m) = bigomega(m) = n.

%I A342109 #17 May 07 2025 12:35:55
%S A342109 7,95,994,9982,99858,999570,9998142,99953490,999068070,9592993410
%N A342109 Largest positive integer m with n digits and such that omega(m) = bigomega(m) = n.
%C A342109 Equivalently: largest n-digit squarefree number with n distinct prime factors (A167050).
%C A342109 Differs from A036337 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 A342109 Differs from A070843 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 A342109 The first index for which these three sequences give three distinct terms is 4:
%C A342109 -> a(4) = 9982 = 2 * 7 * 23 * 31 with omega(9982) = bigomega(9982) = 4.
%C A342109 -> A036337(4) = 9999 = 3 * 3 * 11* 101 with bigomega(9999) = 4 > omega(9999) = 3.
%C A342109 -> A070843(4) = 9996 = 2^2 * 3 * 7^2 *17 with omega(9996) = 4 < bigomega(9996) = 6.
%C A342109 As these terms are the largest n-digit numbers in A167050 that is finite, this sequence is also finite with 10 terms, as for A070843.
%e A342109 9592993410 = 2 * 3 * 5 * 7 * 11 * 13 * 17 * 19 * 23 * 43 and length(9592993410) = omega(9592993410) = bigomega(9592993410) = 10, so, a(10) = 9592993410 is a term; it is also the largest squarefree number with as many decimal digits as distinct prime factors (A167050).
%t A342109 a={}; For[n=1,n<=10,n++,For[m=10^n-1,m>=10^(n-1),m--,If[PrimeOmega[m]==PrimeNu[m]==n,AppendTo[a, m];Break[]]]]; a (* _Stefano Spezia_, Mar 06 2021 *)
%Y A342109 Subsequence of A167050.
%Y A342109 Cf. A001221, A001222, A055642.
%Y A342109 Cf. A036337, A070843, A342108.
%K A342109 nonn,base,fini,full
%O A342109 1,1
%A A342109 _Bernard Schott_, Feb 28 2021