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

7, 95, 994, 9982, 99858, 999570, 9998142, 99953490, 999068070, 9592993410

Offset: 1

Author

Bernard Schott, Feb 28 2021

Keywords

• nonn
• base
• fini
• full

Comments

Equivalently: largest n-digit squarefree number with n distinct prime factors (A167050).

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).

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).

The first index for which these three sequences give three distinct terms is 4:

-> a(4) = 9982 = 2 * 7 * 23 * 31 with omega(9982) = bigomega(9982) = 4.

-> A036337(4) = 9999 = 3 * 3 * 11* 101 with bigomega(9999) = 4 > omega(9999) = 3.

-> A070843(4) = 9996 = 2^2 * 3 * 7^2 *17 with omega(9996) = 4 < bigomega(9996) = 6.

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.

Examples

			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).
		

Crossrefs

Subsequence of A167050.

Cf. A001221, A001222, A055642.

Cf. A036337, A070843, A342108.

Programs

Mathematica

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 *)