A334023 Sum of unitary divisors of n that are larger than sqrt(n).

0, 2, 3, 4, 5, 9, 7, 8, 9, 15, 11, 16, 13, 21, 20, 16, 17, 27, 19, 25, 28, 33, 23, 32, 25, 39, 27, 35, 29, 61, 31, 32, 44, 51, 42, 45, 37, 57, 52, 48, 41, 84, 43, 55, 54, 69, 47, 64, 49, 75, 68, 65, 53, 81, 66, 64, 76, 87, 59, 107, 61, 93, 72, 64, 78, 132, 67

Offset

1,2

Links

Jinyuan Wang, Table of n, a(n) for n = 1..10000

Formula

a(n) = A238535(n) for squarefree numbers (A005117) or squares of primes (A001248).

Example

The unitary divisors of 12 are {1, 3, 4, 12}, 4 and 12 are larger than sqrt(12) and their sum is 4 + 12 = 16, hence a(12) = 16.

Mathematica

a[n_] := DivisorSum[n, # &, #^2 > n && CoprimeQ[#, n/#] &]; Array[a, 100]

Prog

(PARI) a(n) = sumdiv(n, d, if(gcd(d, n/d)==1 && d>sqrt(n), d)); \\ Jinyuan Wang, Apr 12 2020

Crossrefs

Cf. A034448, A077610, A238535, A334019.

Sequence in context: A222251 A347759 A241916 * A079871 A273291 A130064

Adjacent sequences: A334020 A334021 A334022 * A334024 A334025 A334026

Keyword

nonn

Author

Amiram Eldar, Apr 12 2020

Status

approved