A344137 Sum of the squarefree divisors of n whose square does not divide n.

0, 2, 3, 0, 5, 11, 7, 0, 0, 17, 11, 9, 13, 23, 23, 0, 17, 8, 19, 15, 31, 35, 23, 9, 0, 41, 0, 21, 29, 71, 31, 0, 47, 53, 47, 0, 37, 59, 55, 15, 41, 95, 43, 33, 20, 71, 47, 9, 0, 12, 71, 39, 53, 8, 71, 21, 79, 89, 59, 69, 61, 95, 28, 0, 83, 143, 67, 51, 95, 143, 71, 0, 73

Offset

1,2

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Formula

a(n) = Sum_{d|n} d * mu(d)^2 * c(n/d^2), where c(n) = ceiling(n) - floor(n).

a(n) = A048250(n) - A295295(n). - Amiram Eldar, Oct 13 2023

Example

a(20) = Sum_{d|20} d * mu(d)^2 * c(20/d^2) = 1*1*0 + 2*1*0 + 4*0*1 + 5*1*1 + 10*1*1 + 20*0*1 = 15.

Mathematica

a[n_] := DivisorSum[n, # &, SquareFreeQ[#] && ! Divisible[n, #^2] &]; Array[a, 100] (* Amiram Eldar, Oct 13 2023 *)

Prog

(PARI) a(n) = {my(f = factor(n)); prod(i = 1, #f~, f[i, 1] + 1) - prod(i = 1, #f~, if(f[i, 2] == 1, 1, f[i, 1] + 1)); } \\ Amiram Eldar, Oct 13 2023

Crossrefs

Cf. A048250, A295295, A345320.

Sequence in context: A364574 A122830 A375328 * A350260 A358276 A321296

Adjacent sequences: A344134 A344135 A344136 * A344138 A344139 A344140

Keyword

nonn,easy

Author

Wesley Ivan Hurt, Jun 16 2021

Status

approved