A344405 - OEIS

%I #7 May 17 2021 17:56:08

%S 1,4,9,18,25,39,49,72,84,110,121,166,169,217,230,292,289,372,361,455,

%T 455,539,529,670,630,754,756,889,841,1041,961,1168,1122,1292,1232,

%U 1530,1369,1615,1573,1828,1681,2037,1849,2200,2109,2369,2209,2716,2408,2820,2686

%N a(n) = Sum_{d|n} (n/d) * floor(n/d^2).

%C If p is prime, a(p) = Sum_{d|p} (p/d) * floor(p/d^2) = p*p + 1*0 = p^2.

%e a(4) = 18; Sum_{d|4} (4/d) * floor(4/d^2) = 4*4 + 2*1 + 1*0 = 18.

%t Table[Sum[(1 - Ceiling[n/k] + Floor[n/k]) (n/k) Floor[n/k^2], {k, n}], {n, 100}]

%o (PARI) a(n) = sumdiv(n, d, (n/d)*(n\d^2)); \\ _Michel Marcus_, May 17 2021

%Y Cf. A344128, A344403, A344404.

%K nonn

%O 1,2

%A _Wesley Ivan Hurt_, May 16 2021