cp's OEIS Frontend

A343803 a(n) = Sum_{k=1..n} k * (number of divisors of n <= k).

%I A343803 #9 Sep 21 2022 08:55:21
%S A343803 1,5,9,23,20,65,35,109,96,164,77,377,104,307,362,525,170,818,209,1008,
%T A343803 690,725,299,2005,665,1000,1122,1939,464,3106,527,2517,1658,1682,1894,
%U A343803 5084,740,2089,2298,5500,902,6022,989,4701,5066,3035,1175,10117,2478,6069,3890,6532,1484
%N A343803 a(n) = Sum_{k=1..n} k * (number of divisors of n <= k).
%C A343803 If n is prime, then a(n) = n*(n+3)/2.
%F A343803 a(n) = Sum_{k=1..n} Sum_{i=1..k} k * (1 - ceiling(n/i) + floor(n/i)).
%e A343803 a(4) = 1*(1) + 2*(2) + 3*(2) + 4*(3) = 23, i.e.,
%e A343803   (1 times the number of divisors of 4 that are less than or equal to 1)
%e A343803 + (2 times the number of divisors of 4 that are less than or equal to 2)
%e A343803 + (3 times the number of divisors of 4 that are less than or equal to 3)
%e A343803 + (4 times the number of divisors of 4 that are less than or equal to 4).
%t A343803 Table[Sum[Sum[k (1 - Ceiling[n/i] + Floor[n/i]), {i, k}], {k, n}], {n, 60}]
%o A343803 (PARI) a(n) = my(d=divisors(n)); sum(k=1, n, k*#select(x->(x<=k), d)); \\ _Michel Marcus_, Apr 30 2021
%Y A343803 Cf. A081307.
%K A343803 nonn
%O A343803 1,2
%A A343803 _Wesley Ivan Hurt_, Apr 29 2021