A239668 Sum of the composite divisors of n^2.
0, 4, 9, 28, 25, 85, 49, 124, 117, 209, 121, 397, 169, 389, 394, 508, 289, 841, 361, 953, 730, 917, 529, 1645, 775, 1265, 1089, 1757, 841, 2810, 961, 2044, 1714, 2129, 1754, 3745, 1369, 2645, 2362, 3929, 1681, 5174, 1849, 4109, 3742, 3845, 2209, 6637, 2793, 5459, 3970
Offset: 1
Keywords
Examples
For n=2, the sum of the composite factors of n^2 is equal to 4.
Links
- Harvey P. Dale, Table of n, a(n) for n = 1..1000
Programs
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Maple
A008472 := n -> add(d, d = select(isprime, numtheory[divisors](n))): f:=n->numtheory[sigma](n^2)-A008472(n)-1; [seq(f(n),n=1..100)]; # N. J. A. Sloane, Mar 31 2014
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Mathematica
a[n_] := DivisorSum[n^2, If[# == 1 || PrimeQ[#], 0, #]& ]; Array[a, 60] (* Jean-François Alcover, Dec 18 2015 *) Table[Total[Select[Divisors[n^2],CompositeQ]],{n,60}] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jul 06 2017 *)
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PARI
a(n) = sumdiv(n^2, d, d*(!isprime(d) && (d != 1))); \\ Michel Marcus, Mar 31 2014
Formula
a(n) = sigma(n^2) - sopf(n^2) - 1.
a(n) = A023891(n^2). - Michel Marcus, Mar 31 2014
a(n) = n^2 if n is prime. - Zak Seidov, Mar 31 2014
Extensions
Formula corrected by Wesley Ivan Hurt, Mar 30 2014
More terms from N. J. A. Sloane, Mar 31 2014