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A239668
Sum of the composite divisors of n^2.
1
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
1,2
LINKS
FORMULA
a(n) = sigma(n^2) - sopf(n^2) - 1.
a(n) = A000203(n^2) - A008472(n^2) - 1. - Wesley Ivan Hurt, Mar 30 2014
a(n) = A023891(n^2). - Michel Marcus, Mar 31 2014
a(n) = n^2 if n is prime. - Zak Seidov, Mar 31 2014
EXAMPLE
For n=2, the sum of the composite factors of n^2 is equal to 4.
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
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 *)
PROG
(PARI) a(n) = sumdiv(n^2, d, d*(!isprime(d) && (d != 1))); \\ Michel Marcus, Mar 31 2014
CROSSREFS
KEYWORD
nonn
AUTHOR
Janet Lee, Mar 23 2014
EXTENSIONS
Formula corrected by Wesley Ivan Hurt, Mar 30 2014
More terms from N. J. A. Sloane, Mar 31 2014
STATUS
approved