A175067 a(n) is the sum of perfect divisors of n, where a perfect divisor of n is a divisor d such that d^k = n for some k >= 1.

1, 2, 3, 6, 5, 6, 7, 10, 12, 10, 11, 12, 13, 14, 15, 22, 17, 18, 19, 20, 21, 22, 23, 24, 30, 26, 30, 28, 29, 30, 31, 34, 33, 34, 35, 42, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 56, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 78, 65, 66, 67, 68, 69, 70, 71, 72

Offset

1,2

Comments

a(n) > n for perfect powers n = A001597(m) for m > 2.

Links

Ivan Neretin, Table of n, a(n) for n = 1..10000

Formula

a(n) = A175070(n) + n. [Jaroslav Krizek, Jan 24 2010]

Example

For n = 8: a(8) = 10; there are two perfect divisors of 8: 2 and 8; their sum is 10.

Mathematica

Table[Plus @@ (n^(1/Divisors[GCD @@ FactorInteger[n][[All, 2]]])), {n, 72}] (* Ivan Neretin, May 13 2015 *)

Crossrefs

Sequence in context: A093783 A096861 A118738 * A361174 A323309 A322857

Adjacent sequences: A175064 A175065 A175066 * A175068 A175069 A175070

Keyword

nonn

Author

Jaroslav Krizek, Jan 23 2010

Extensions

Name edited by Michel Marcus, Jun 13 2018

Status

approved