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

%I A342173 #29 Jan 09 2025 00:22:17
%S A342173 0,1,3,6,11,14,20,23,30,39,43,53,60,64,71,81,92,96,107,115,118,130,
%T A342173 136,148,164,171,175,183,186,194,222,229,241,245,265,269,282,293,301,
%U A342173 313,325,329,351,354,362,366,392,417,424,428,437,450,454,473,485,498,511
%N A342173 a(n) = Sum_{j=1..n-1} floor(prime(n)/prime(j)).
%C A342173 a(n) is the sum of the quotients in integer division of prime(n) by all smaller primes.
%H A342173 Robert Israel, <a href="/A342173/b342173.txt">Table of n, a(n) for n = 1..10000</a>
%H A342173 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 A342173 a(n) = A308495(n) - 2. - _Hugo Pfoertner_, Mar 04 2021
%F A342173 a(n) = A013939(A006093(n)). - _Flávio V. Fernandes_, Jan 03 2025
%e A342173 a(4) = floor(7/2) + floor(7/3) + floor(7/5) = 6.
%p A342173 f:= proc(n) local t,i,s;
%p A342173   t:= ithprime(n);
%p A342173   add(floor(t/ ithprime(i)),i=1..n-1)
%p A342173 end proc:
%p A342173 map(f, [$1..100]);
%t A342173 Table[Sum[Floor[Prime[n]/Prime[j]],{j,n-1}],{n,64}] (* _Stefano Spezia_, Mar 04 2021 *)
%o A342173 (PARI) a(n) = sum(j=1, n-1, prime(n)\prime(j)); \\ _Michel Marcus_, Mar 04 2021
%Y A342173 Cf. A033955, A006093, A013939, A308495.
%K A342173 nonn
%O A342173 1,3
%A A342173 _J. M. Bergot_ and _Robert Israel_, Mar 03 2021