A345451 - OEIS

A345451

Sum of the unitary divisors of n whose square does not divide n.

0, 2, 3, 4, 5, 11, 7, 8, 9, 17, 11, 19, 13, 23, 23, 16, 17, 29, 19, 29, 31, 35, 23, 35, 25, 41, 27, 39, 29, 71, 31, 32, 47, 53, 47, 49, 37, 59, 55, 53, 41, 95, 43, 59, 59, 71, 47, 67, 49, 77, 71, 69, 53, 83, 71, 71, 79, 89, 59, 119, 61, 95, 79, 64, 83, 143, 67, 89, 95, 143, 71

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OFFSET

1,2

COMMENTS

a(p) = p for primes p.

LINKS

Table of n, a(n) for n=1..71.

FORMULA

a(n) = Sum_{d|n, gcd(d,n/d)=1} d * (ceiling(n/d^2)-floor(n/d^2)).

a(n) = A034448(n)-1. - Chai Wah Wu, Jun 20 2021

MATHEMATICA

a[n_] := -1 + Times @@ (1 + Power @@@ FactorInteger[n]); a[1] = 0; Array[a, 71] (* Amiram Eldar, Aug 31 2026 *)