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

Author

Amiram Eldar, Apr 12 2020

Keywords

• nonn

Examples

			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.
		

Links

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

Crossrefs

Cf. A034448, A077610, A238535, A334019.

Programs

Mathematica

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

PARI

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

Formula

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