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

1,6

Links

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

Formula

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

Example

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.

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, A070039, A077610, A334023.

Sequence in context: A183093 A183096 A029356 * A291448 A114006 A050328

Adjacent sequences: A334016 A334017 A334018 * A334020 A334021 A334022

Keyword

nonn

Author

Amiram Eldar, Apr 12 2020

Status

approved