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

1,2

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

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

Sequence in context: A144652 A035493 A363277 * A328638 A327420 A119790

Adjacent sequences: A070035 A070036 A070037 * A070039 A070040 A070041

Keyword

nonn

Author

Labos Elemer, Apr 19 2002

Status

approved