I just have a quick inquiry about the Wolfram MathWorld entry on Odd Perfect Number.
Last sentence of the fifth paragraph states that:
Hagis (1980) showed that odd perfect numbers must have at least eight distinct prime factors, in which case, the number is divisible by 15 (Voight 2003).
Since Nielsen (2015) has already proved that odd perfect numbers must have at least ten distinct prime factors, does this mean that they must be divisible by $15$?
Upon inspecting Voight's paper, I was under the impression that the divisibility-by-5 condition only holds for odd perfect numbers with exactly eight distinct prime factors.
Can anybody confirm if my impression is correct?
Hagis, P. Jr. "An Outline of a Proof that Every Odd Perfect Number has at Least Eight Prime Factors." Math. Comput. 34, 1027-1032, 1980.
Voight, J. "On the Nonexistence of Odd Perfect Numbers." MASS Selecta. Providence, RI: Amer. Math. Soc., pp. 293-300, 2003.
Nielsen, P. P. "Odd perfect numbers, Diophantine equations, and upper bounds", Math. Comp. 84, 2549-2567, 2015.