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

1,2

Comments

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

Links

Table of n, a(n) for n=1..69.

Example

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

Mathematica

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

Prog

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

Crossrefs

Cf. A344128, A344404, A344405.

Sequence in context: A023852 A354629 A048750 * A326136 A276081 A329564

Adjacent sequences: A344400 A344401 A344402 * A344404 A344405 A344406

Keyword

nonn

Author

Wesley Ivan Hurt, May 16 2021

Status

approved