A334019 - OEIS

%I #10 Apr 13 2020 07:19:10

%S 0,1,1,1,1,3,1,1,1,3,1,4,1,3,4,1,1,3,1,5,4,3,1,4,1,3,1,5,1,11,1,1,4,3,

%T 6,5,1,3,4,6,1,12,1,5,6,3,1,4,1,3,4,5,1,3,6,8,4,3,1,13,1,3,8,1,6,12,1,

%U 5,4,15,1,9,1,3,4,5,8,12,1,6,1,3,1,15,6

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

%H Jinyuan Wang, <a href="/A334019/b334019.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = A070039(n) for squarefree numbers (A005117) or squares of primes (A001248).

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

%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, A070039, A077610, A334023.

%K nonn

%O 1,6

%A _Amiram Eldar_, Apr 12 2020