A070038 - OEIS

%I #23 Dec 28 2017 07:56:41

%S 1,2,3,6,5,9,7,12,12,15,11,22,13,21,20,28,17,33,19,35,28,33,23,50,30,

%T 39,36,49,29,61,31,56,44,51,42,81,37,57,52,78,41,84,43,77,69,69,47,

%U 108,56,85,68,91,53,108,66,106,76,87,59,147,61,93,93,120,78,132,67,119,92

%N a(n) = sum of divisors of n that are at least sqrt(n).

%C a(n) = n iff n is not a composite number.

%C Sum of a subset of all divisors of n, not including complementary divisors of any term.

%H Seiichi Manyama, <a href="/A070038/b070038.txt">Table of n, a(n) for n = 1..10000</a>

%e a(20) = 35: the divisors of 20 are 1,2,4,5,10 and 20. a(20) = 5 + 10 + 20 = 35.

%e a(96) = 228 = 96 + 48 + 32 + 24 + 16 + 12 (sum of an even number of divisors);

%e a(225) = 385 = 225 + 75 + 45 + 25 + 15 (sum of an odd number of divisors).

%p 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);

%t Table[Plus @@ Select[Divisors[n], # >= Sqrt[n] &], {n, 1, 70}]

%o (Sage) [sum(k for k in divisors(n) if k^2>=n) for n in range (1,70)] # _Giuseppe Coppoletta_, Jan 21 2015

%o (PARI) a(n) = sumdiv(n, d, d*(d^2>=n)); \\ _Michel Marcus_, Jan 22 2015

%Y Cf. A038548, A000203, A000005, A070039, A056924, A072500, A066839.

%K nonn

%O 1,2

%A _Labos Elemer_, Apr 19 2002