A334019 Sum of unitary divisors of n that are smaller than sqrt(n).

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

Offset: 1

Author

Amiram Eldar, Apr 12 2020

Keywords

• nonn

Examples

			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.
		

Links

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

Crossrefs

Cf. A034448, A070039, A077610, A334023.

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 && dJinyuan Wang, Apr 12 2020

Formula

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