A342173 - OEIS

%I #29 Jan 09 2025 00:22:17

%S 0,1,3,6,11,14,20,23,30,39,43,53,60,64,71,81,92,96,107,115,118,130,

%T 136,148,164,171,175,183,186,194,222,229,241,245,265,269,282,293,301,

%U 313,325,329,351,354,362,366,392,417,424,428,437,450,454,473,485,498,511

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

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

%H Robert Israel, <a href="/A342173/b342173.txt">Table of n, a(n) for n = 1..10000</a>

%H Lorenzo Sauras-Altuzarra, <a href="https://doi.org/10.26493/2590-9770.1473.ec5">Some properties of the factors of Fermat numbers</a>, Art Discrete Appl. Math. (2022).

%F a(n) = A308495(n) - 2. - _Hugo Pfoertner_, Mar 04 2021

%F a(n) = A013939(A006093(n)). - _Flávio V. Fernandes_, Jan 03 2025

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

%p f:= proc(n) local t,i,s;

%p   t:= ithprime(n);

%p   add(floor(t/ ithprime(i)),i=1..n-1)

%p end proc:

%p map(f, [$1..100]);

%t Table[Sum[Floor[Prime[n]/Prime[j]],{j,n-1}],{n,64}] (* _Stefano Spezia_, Mar 04 2021 *)

%o (PARI) a(n) = sum(j=1, n-1, prime(n)\prime(j)); \\ _Michel Marcus_, Mar 04 2021

%Y Cf. A033955, A006093, A013939, A308495.

%K nonn,changed

%O 1,3

%A _J. M. Bergot_ and _Robert Israel_, Mar 03 2021