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odd naturals with indicator same as 1990 (Chile NMO 1990 P2)

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November 20, 2021
number theory

Problem Statement

Find all the odd naturals whose indicator is the same as 19901990.
We clarify that, if a natural decomposes into prime factors in the form Πj=1rpjaj\Pi_{j=1}^r p_j^{a_j}, define the indicator as : ϕ(n)=rΠj=1rpjaj−1(pj+1)\phi (n) = r\Pi_{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.
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