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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 (list; graph; refs; listen; history; text; internal format)
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
Sequence in context: A087726 A270891 A272313 * A101973 A244968 A071258
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

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Last modified March 29 10:59 EDT 2024. Contains 371277 sequences. (Running on oeis4.)