A344404 -id:A344404 - cp's OEIS frontend

A344403 a(n) = Sum_{d|n} d * floor(n/d^2).

1, 2, 3, 6, 5, 8, 7, 12, 12, 14, 11, 21, 13, 20, 18, 28, 17, 32, 19, 34, 27, 32, 23, 46, 30, 38, 36, 46, 29, 58, 31, 56, 42, 50, 40, 80, 37, 56, 51, 73, 41, 80, 43, 74, 65, 68, 47, 105, 56, 84, 66, 90, 53, 104, 65, 103, 75, 86, 59, 136, 61, 92, 91, 120, 75, 125, 67, 118, 90

Offset: 1

Wesley Ivan Hurt, May 16 2021

nonn

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

			a(6) = 8; Sum_{d|6} d * floor(6/d^2) = 1*6 + 2*1 + 3*0 + 6*0 = 8.

Cf. A344128, A344404, A344405.

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

a(n) = sumdiv(n, d, d*(n\d^2)); \\ Michel Marcus, May 17 2021

G.f.: Sum_{k>=1} k*x^(k^2)/((1 - x^k)*(1 - x^(k^2))). - Miles Wilson, Jun 11 2025

A344405 a(n) = Sum_{d|n} (n/d) * floor(n/d^2).

Original entry on oeis.org

1, 4, 9, 18, 25, 39, 49, 72, 84, 110, 121, 166, 169, 217, 230, 292, 289, 372, 361, 455, 455, 539, 529, 670, 630, 754, 756, 889, 841, 1041, 961, 1168, 1122, 1292, 1232, 1530, 1369, 1615, 1573, 1828, 1681, 2037, 1849, 2200, 2109, 2369, 2209, 2716, 2408, 2820, 2686

Offset: 1

Wesley Ivan Hurt, May 16 2021

nonn

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

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

Cf. A344128, A344403, A344404.

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

a(n) = sumdiv(n, d, (n/d)*(n\d^2)); \\ Michel Marcus, May 17 2021

cp's OEIS Frontend

A344403 a(n) = Sum_{d|n} d * floor(n/d^2).

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