A070038 a(n) = sum of divisors of n that are at least sqrt(n).

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, 39, 36, 49, 29, 61, 31, 56, 44, 51, 42, 81, 37, 57, 52, 78, 41, 84, 43, 77, 69, 69, 47, 108, 56, 85, 68, 91, 53, 108, 66, 106, 76, 87, 59, 147, 61, 93, 93, 120, 78, 132, 67, 119, 92

Offset: 1

Author

Labos Elemer, Apr 19 2002

Keywords

• nonn

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.

Examples

			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).
		

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..10000

Crossrefs

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

Programs

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}]

PARI

a(n) = sumdiv(n, d, d*(d^2>=n)); \\ Michel Marcus, Jan 22 2015

Sage

[sum(k for k in divisors(n) if k^2>=n) for n in range (1,70)] # Giuseppe Coppoletta, Jan 21 2015