A345451 - OEIS

%I #7 Jun 20 2021 19:18:55

%S 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,

%T 41,27,39,29,71,31,32,47,53,47,49,37,59,55,53,41,95,43,59,59,71,47,67,

%U 49,77,71,69,53,83,71,71,79,89,59,119,61,95,79,64,83,143,67,89,95,143,71

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

%C a(p) = p for primes p.

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

%F a(n) = A034448(n)-1. - _Chai Wah Wu_, Jun 20 2021

%o (Python 3.8+)

%o from math import prod

%o from sympy import factorint

%o def A345451(n): return prod(p**e+1 for p, e in factorint(n).items())-1 # _Chai Wah Wu_, Jun 20 2021

%Y Cf. A034448.

%K nonn

%O 1,2

%A _Wesley Ivan Hurt_, Jun 19 2021