A384936 a(n) = Sum_{k=1..n} floor( log(A002110(n)) / log(prime(k)) ).
0, 1, 3, 9, 16, 28, 42, 57, 76, 97, 121, 148, 177, 208, 242, 279, 316, 359, 401, 446, 493, 545, 596, 651, 708, 767, 829, 893, 958, 1026, 1096, 1170, 1246, 1319, 1400, 1484, 1567, 1657, 1742, 1834, 1923, 2021, 2119, 2218, 2316, 2419, 2526, 2635, 2745, 2857, 2972
Offset: 0
Examples
Table of n, a(n) for n = 0..10, listing terms in row n of A287010:
Terms in row n of A287010 corresponding
to the primes listed in the header
n\k 2 3 5 7 11 13 17 19 23 29 a(n)
---------------------------------------------------
0: 0 . . . . . . . . . 0
1: 1 . . . . . . . . . 1
2: 2 1 . . . . . . . . 3
3: 4 3 2 . . . . . . . 9
4: 7 4 3 2 . . . . . . 16
5: 11 7 4 3 3 . . . . . 28
6: 14 9 6 5 4 4 . . . . 42
7: 18 11 8 6 5 5 4 . . . 57
8: 23 14 9 8 6 6 5 5 . . 76
9: 27 17 11 9 8 7 6 6 6 . 97
10: 32 20 14 11 9 8 7 7 7 6 121
Links
- Michael De Vlieger, Table of n, a(n) for n = 0..10000
Programs
-
Mathematica
P = 2; s = {2}; {0}~Join~Reap[Do[Sow@ Total@ Map[Floor@ Log[#, P] &, s]; (AppendTo[s, #]; P *= #) &[Prime[k]], {k, 2, 51}] ][[-1, 1]] -
PARI
a(n) = my(v=primes(n), pp=vecprod(v)); sum(k=1, n, log(pp)\log(v[k])); \\ Michel Marcus, Jun 14 2025
Comments