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

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

Prog

(Python 3.8+)
from math import prod
from sympy import factorint
def A345451(n): return prod(p**e+1 for p, e in factorint(n).items())-1 # Chai Wah Wu, Jun 20 2021

Crossrefs

Cf. A034448.

Sequence in context: A247233 A329906 A325651 * A345320 A160000 A245448

Adjacent sequences: A345448 A345449 A345450 * A345452 A345453 A345454

Keyword

nonn

Author

Wesley Ivan Hurt, Jun 19 2021

Status

approved