A385863 a(n) is the largest number of distinct prime factors a number with at most n digits can have.

2, 3, 4, 5, 6, 7, 8, 8, 9, 10, 10, 11, 12, 12, 13, 13, 14, 15, 15, 16, 16, 17, 17, 18, 19, 19, 20, 20, 21, 21, 22, 22, 23, 23, 24, 24, 25, 25, 26, 26, 27, 27, 28, 28, 29, 29, 30, 30, 31, 31, 32, 32, 33, 33, 33, 34, 34, 35, 35, 36, 36, 37, 37, 38, 38, 39, 39, 39, 40

Offset

1,1

Comments

Also the largest k such that primorial(k) < 10^n.

"at most" in name could also be "exactly" and it gives the same data.

a(n) is the number of distinct prime factors of A091800(n).

Links

Paolo Xausa, Table of n, a(n) for n = 1..10000

Formula

a(n) = A001221(A091800(n)).

Example

a(5) = 6 as primorial(6) = 30030 < 10^5 < 510510 = primorial(6 + 1) = primorial(7).

Mathematica

Table[First[FirstPosition[#, _?(# > n &)]] - 1, {n, Last[#] - 1}] & [IntegerLength[FoldList[Times, Prime[Range[50]]]]] (* Paolo Xausa, Aug 20 2025 *)

Prog

(PARI) a(n) = my(ulim=10^n-1, pp=1, t=0); forprime(p=2, oo, pp*=p; if(pp > ulim, return(t)); t++)

Crossrefs

Cf. A001221, A002110, A002283, A067175, A091800, A387173.

Sequence in context: A079631 A347623 A269849 * A228881 A252373 A245338

Adjacent sequences: A385860 A385861 A385862 * A385864 A385865 A385866

Keyword

nonn,easy,base

Author

David A. Corneth, Aug 20 2025

Status

approved