A387173 -id:A387173 - cp's OEIS frontend

A067175 Number of digits in the n-th primorial (A002110).

1, 1, 1, 2, 3, 4, 5, 6, 7, 9, 10, 12, 13, 15, 17, 18, 20, 22, 24, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 56, 58, 60, 62, 64, 66, 69, 71, 73, 76, 78, 80, 82, 85, 87, 89, 92, 94, 97, 99, 101, 104, 106, 109, 111, 113, 116, 118, 121, 123, 126, 128, 131, 133

Offset: 0

Lekraj Beedassy, Feb 18 2002

Alois P. Heinz, Table of n, a(n) for n = 0..10000 (first 5001 terms from Soumyadeep Dhar)

Cf. A002110. Essentially the same as A048856.

Cf. A004216, A004218, A055642, A387173.

with(numtheory): it := 1: for n from 1 to 150 do it := it*ithprime(n): printf(`%d,`,ceil(log[10](it))) od:

Table[Floor[Log[10, Product[Prime[k], {k, n}]] + 1], {n, 0, 67}]
Join[{1},IntegerLength/@FoldList[Times,Prime[Range[70]]]] (* Harvey P. Dale, Jan 03 2024 *)

a(n) = 1 + logint(vecprod(primes(n)), 10) \\ Andrew Howroyd, Apr 24 2021

from sympy import primorial
def a(n): return 1 if n == 0 else len(str(primorial(n)))
print([a(n) for n in range(68)]) # Michael S. Branicky, Apr 24 2021

Edited and extended by Robert G. Wilson v and James Sellers, Feb 19 2002

Offset corrected by Arkadiusz Wesolowski, May 04 2013

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

Original entry on oeis.org

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

David A. Corneth, Aug 20 2025

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).

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

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

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

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

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

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

cp's OEIS Frontend

A067175 Number of digits in the n-th primorial (A002110).

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