A085302 a(n) is the partial sum of A085301(j) from j=1 to n; a(n)-1 shows the number of factorials below n-th primorial.
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
Offset: 1
Examples
For n = 26: a(26) = 34 since there are 33 factorials below the 26th primorial.
Links
- Amiram Eldar, Table of n, a(n) for n = 1..10000
Programs
-
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 *)