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A342173
a(n) = Sum_{j=1..n-1} floor(prime(n)/prime(j)).
3
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
1,3
COMMENTS
a(n) is the sum of the quotients in integer division of prime(n) by all smaller primes.
LINKS
Lorenzo Sauras-Altuzarra, Some properties of the factors of Fermat numbers, Art Discrete Appl. Math. (2022).
FORMULA
a(n) = A308495(n) - 2. - Hugo Pfoertner, Mar 04 2021
EXAMPLE
a(4) = floor(7/2) + floor(7/3) + floor(7/5) = 6.
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 *)
PROG
(PARI) a(n) = sum(j=1, n-1, prime(n)\prime(j)); \\ Michel Marcus, Mar 04 2021
CROSSREFS
Cf. A033955.
Sequence in context: A047924 A267519 A200182 * A282277 A122599 A342954
KEYWORD
nonn
AUTHOR
J. M. Bergot and Robert Israel, Mar 03 2021
STATUS
approved