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

0,3

Comments

A384442(a(n)) = A002110(n) for n <= 8; does it hold for n > 5?

Links

Michael De Vlieger, Table of n, a(n) for n = 0..10000

Formula

a(n) = A361373(A002110(n)).

Row sums of A287010.

Example

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

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]]

Prog

(PARI) a(n) = my(v=primes(n), pp=vecprod(v)); sum(k=1, n, log(pp)\log(v[k])); \\ Michel Marcus, Jun 14 2025

Crossrefs

Cf. A002110, A287010, A361373, A377485, A384442.

Sequence in context: A061942 A174440 A244475 * A212870 A306447 A257034

Adjacent sequences: A384933 A384934 A384935 * A384937 A384938 A384939

Keyword

nonn,easy

Author

Michael De Vlieger, Jun 12 2025

Status

approved