OFFSET
1,2
COMMENTS
LINKS
Antti Karttunen, Table of n, a(n) for n = 1..10080
Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537
FORMULA
a(n) = Sum_{d|n, d<n} d+(A008966(n/d) * d).
For squarefree n, a(n) = 2*A001065(n).
Sum_{k=1..n} a(k) = c * n^2 / 2 + O(n*log(n)), where c = Pi^2/6 + 15/Pi^2 - 2 = 1.164751... . - Amiram Eldar, Dec 08 2023
MATHEMATICA
a[n_] := Sum[d + If[SquareFreeQ[n/d], d, 0], {d, Most[Divisors[n]]}];
Array[a, 100] (* Jean-François Alcover, Jun 12 2021 *)
PROG
(PARI) A344753(n) = sumdiv(n, d, (d<n)*(d+(issquarefree(n/d) * d)));
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Antti Karttunen, May 28 2021
EXTENSIONS
New primary definition added by Antti Karttunen, Jun 06 2021
STATUS
approved