cp's OEIS Frontend

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.

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A070842 Smallest n-digit number with exactly n prime divisors. There are no further terms.

Original entry on oeis.org

2, 10, 102, 1020, 10010, 101010, 1009470, 11741730, 223092870, 6469693230
Offset: 1

Views

Author

Amarnath Murthy, May 12 2002

Keywords

Examples

			a(4) = 1020 with the prime divisors 2, 3, 5, 17.

Crossrefs

Cf. A001221 (omega), A002110 (primorials), A070843.

Extensions

More terms from Robert G. Wilson v and Rick L. Shepherd, May 14 2002
Corrected and edited by Ray Chandler, Feb 15 2009

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

Original entry on oeis.org

7, 95, 994, 9982, 99858, 999570, 9998142, 99953490, 999068070, 9592993410
Offset: 1

Views

Author

Bernard Schott, Feb 28 2021

Keywords

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 *)
Showing 1-2 of 2 results.

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