A new upper bound for odd perfect numbers of a special form

@article{Yamada2019ANU,
  title={A new upper bound for odd perfect numbers of a special form},
  author={Tomohiro Yamada},
  journal={Colloquium Mathematicum},
  year={2019}
}
We shall given a new effectively computable upper bound of odd perfect numbers whose Euler factors are powers of fixed exponent, improving our old result in T. Yamada, Colloq. Math. 103 (2005), 303--307. 
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We show that there is an effectively computable upper bound of odd perfect numbers whose Euler factors are powers of fixed exponent.
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This seems simple enough, but let’s play with this definition. The Pythagoreans, an ancient sect of mathematical mystics, said that a number is perfect if it equals the sum of its positive integral
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however (for it was the literal soul of the life of the Redeemer, John xv. io), is the peculiar token of fellowship with the Redeemer. That love to God (what is meant here is not God’s love to men)
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Sind p, qv . . ., qr die in der ungeraden Zahl n aufgehenden verschiedenen Primteiler, so soll gezeigt werden: (1) Satz, n = pqlqlql · · · qr ist nicht vollkommen. Für die Fälle a = l und «. = 5 ist
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In diesem Abschnitt sollen einige Sätze über Kreisteilungspolynome, die an anderer Stelle bewiesen wurden), verallgemeinert und durch einige Größenabschätzungen ergänzt werden. Wir wollen uns dabei
Untersuchungen über ungerade vollkommene Zahlen.
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