A334023 - OEIS

%I #13 Apr 13 2020 07:19:05

%S 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,

%T 27,35,29,61,31,32,44,51,42,45,37,57,52,48,41,84,43,55,54,69,47,64,49,

%U 75,68,65,53,81,66,64,76,87,59,107,61,93,72,64,78,132,67

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

%H Jinyuan Wang, <a href="/A334023/b334023.txt">Table of n, a(n) for n = 1..10000</a>

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

%e 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.

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

%o (PARI) a(n) = sumdiv(n, d, if(gcd(d, n/d)==1 && d>sqrt(n), d)); \\ _Jinyuan Wang_, Apr 12 2020

%Y Cf. A034448, A077610, A238535, A334019.

%K nonn

%O 1,2

%A _Amiram Eldar_, Apr 12 2020