OFFSET
1,2
COMMENTS
a(n) = n iff n is not a composite number.
Sum of a subset of all divisors of n, not including complementary divisors of any term.
LINKS
Seiichi Manyama, Table of n, a(n) for n = 1..10000
EXAMPLE
a(20) = 35: the divisors of 20 are 1,2,4,5,10 and 20. a(20) = 5 + 10 + 20 = 35.
a(96) = 228 = 96 + 48 + 32 + 24 + 16 + 12 (sum of an even number of divisors);
a(225) = 385 = 225 + 75 + 45 + 25 + 15 (sum of an odd number of divisors).
MAPLE
with(numtheory):for n from 1 to 200 do c[n] := 0:d := divisors(n):for i from 1 to nops(d) do if d[i]>=n^.5 then c[n] := c[n]+d[i]:fi:od:od:seq(c[i], i=1..200);
MATHEMATICA
Table[Plus @@ Select[Divisors[n], # >= Sqrt[n] &], {n, 1, 70}]
PROG
(Sage) [sum(k for k in divisors(n) if k^2>=n) for n in range (1, 70)] # Giuseppe Coppoletta, Jan 21 2015
(PARI) a(n) = sumdiv(n, d, d*(d^2>=n)); \\ Michel Marcus, Jan 22 2015
CROSSREFS
KEYWORD
nonn
AUTHOR
Labos Elemer, Apr 19 2002
STATUS
approved