A345264 a(n) = Sum_{d|n} rad(d) * mu(n/d)^2.

1, 3, 4, 4, 6, 12, 8, 4, 6, 18, 12, 16, 14, 24, 24, 4, 18, 18, 20, 24, 32, 36, 24, 16, 10, 42, 6, 32, 30, 72, 32, 4, 48, 54, 48, 24, 38, 60, 56, 24, 42, 96, 44, 48, 36, 72, 48, 16, 14, 30, 72, 56, 54, 18, 72, 32, 80, 90, 60, 96, 62, 96, 48, 4, 84, 144, 68, 72, 96, 144, 72, 24

Offset

1,2

Comments

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

Links

Table of n, a(n) for n=1..72.

Example

a(8) = Sum_{d|8} rad(d) * mu(8/d)^2 = 1*0 + 2*0 + 2*1 + 2*1 = 4.

Mathematica

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

Crossrefs

Cf. A007947 (rad).

Sequence in context: A089640 A086659 A265887 * A344465 A008473 A326043

Adjacent sequences: A345261 A345262 A345263 * A345265 A345266 A345267

Keyword

nonn

Author

Wesley Ivan Hurt, Jun 12 2021

Status

approved