A334019 - OEIS

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

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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