A342173 a(n) = Sum_{j=1..n-1} floor(prime(n)/prime(j)).

0, 1, 3, 6, 11, 14, 20, 23, 30, 39, 43, 53, 60, 64, 71, 81, 92, 96, 107, 115, 118, 130, 136, 148, 164, 171, 175, 183, 186, 194, 222, 229, 241, 245, 265, 269, 282, 293, 301, 313, 325, 329, 351, 354, 362, 366, 392, 417, 424, 428, 437, 450, 454, 473, 485, 498, 511

Offset: 1

Author

J. M. Bergot and Robert Israel, Mar 03 2021

Keywords

• nonn

Comments

a(n) is the sum of the quotients in integer division of prime(n) by all smaller primes.

Examples

			a(4) = floor(7/2) + floor(7/3) + floor(7/5) = 6.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000
• Lorenzo Sauras-Altuzarra, Some properties of the factors of Fermat numbers, Art Discrete Appl. Math. (2022).

Crossrefs

Cf. A033955, A006093, A013939, A308495.

Programs

Maple

f:= proc(n) local t,i,s;
  t:= ithprime(n);
  add(floor(t/ ithprime(i)),i=1..n-1)
end proc:
map(f, [$1..100]);

Mathematica

Table[Sum[Floor[Prime[n]/Prime[j]],{j,n-1}],{n,64}] (* Stefano Spezia, Mar 04 2021 *)

PARI

a(n) = sum(j=1, n-1, prime(n)\prime(j)); \\ Michel Marcus, Mar 04 2021

Formula

a(n) = A308495(n) - 2. - Hugo Pfoertner, Mar 04 2021

a(n) = A013939(A006093(n)). - Flávio V. Fernandes, Jan 03 2025