A085302 - OEIS

A085302

Partial sums of A085301.

2, 4, 5, 6, 7, 8, 10, 11, 12, 14, 15, 16, 17, 19, 20, 21, 23, 24, 25, 27, 28, 29, 31, 32, 33, 34, 36, 37, 38, 40, 41, 42, 44, 45, 46, 47, 49, 50, 51, 53, 54, 55, 57, 58, 59, 60, 62, 63, 64, 66, 67, 68, 70, 71, 72, 73, 75, 76, 77, 79, 80, 81, 83, 84, 85, 86, 88, 89, 90, 92, 93

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OFFSET

1,1

COMMENTS

a(n)-1 is the number of factorials below the n-th primorial.

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..10000

EXAMPLE

For n = 26: a(26) = 34 since there are 33 factorials below the 26th primorial.

MATHEMATICA

fn[n_] := Module[{k = 1, r = n}, While[r >= 1, k++; r /= k]; k - 1]; prim[n_] := Times @@ Prime[Range[n]]; a[1] = 2; a[n_] := fn[prim[n]] + 1; Array[a, 100] (* Amiram Eldar, Feb 09 2025 *)

CROSSREFS

Cf. A085301, A002110, A000142.

Variant of A073071 and A048964.

Sequence in context: A287183 A039140 A249031 * A193928 A146215 A385479

Adjacent sequences: A085299 A085300 A085301 * A085303 A085304 A085305

KEYWORD

nonn

AUTHOR

Labos Elemer, Jun 26 2003

EXTENSIONS

Name edited by Sean A. Irvine, Jun 13 2026

STATUS

approved