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
Examples
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.
Links
- Amiram Eldar, Table of n, a(n) for n = 1..10000
Programs
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Mathematica
a[n_] := DivisorSum[n, # &, SquareFreeQ[#] && ! Divisible[n, #^2] &]; Array[a, 100] (* Amiram Eldar, Oct 13 2023 *)
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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
Formula
a(n) = Sum_{d|n} d * mu(d)^2 * c(n/d^2), where c(n) = ceiling(n) - floor(n).