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National and Regional Contests
Chile Contests
Chile National Olympiad
1990 Chile National Olympiad
2
2
Part of
1990 Chile National Olympiad
Problems
(1)
odd naturals with indicator same as 1990 (Chile NMO 1990 P2)
Source:
11/20/2021
Find all the odd naturals whose indicator is the same as
1990
1990
1990
.We clarify that, if a natural decomposes into prime factors in the form
Π
j
=
1
r
p
j
a
j
\Pi_{j=1}^r p_j^{a_j}
Π
j
=
1
r
p
j
a
j
, define the indicator as :
ϕ
(
n
)
=
r
Π
j
=
1
r
p
j
a
j
−
1
(
p
j
+
1
)
\phi (n) = r\Pi_{j=1}^r p_j^{a_j-1} (p_j + 1)
ϕ
(
n
)
=
r
Π
j
=
1
r
p
j
a
j
−
1
(
p
j
+
1
)
.[hide=official wording for first sentence]Encuentre todos los naturales impares cuyo indicador es el mismo que el de 1990.
number theory