A search procedure and lower bound for odd perfect numbers

Tuckerman, Bryant

doi:10.1090/S0025-5718-1973-0325506-7

A search procedure and lower bound for odd perfect numbers
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Math. Comp. 27 (1973), 943-949 Request permission

Corrigendum: Math. Comp. 28 (1974), 887.
Corrigendum: Math. Comp. 28 (1974), 887.

Abstract:

An infinite tree-generating "q-algorithm" is defined, which if executed would enumerate all odd perfect numbers (opn’s). A truncated execution shows that any opn has either some component ${p^a} > {10^{18}}$, with a even, or no divisor $< 7$; hence any opn must be $> {10^{36}}$.

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Odd Perfect Numbers: A Search Procedure, and a New Lower Bound of

Notices Amer. Math. Soc.

Odd-Perfect-Number Tree to

to accompany ’A Search Procedure and Lower Bound for Odd Perfect Numbers.’

Peter Hagis Jr., A lower bound for the set of odd perfect numbers, Math. Comp. 27 (1973), 951–953. MR 325507, DOI 10.1090/S0025-5718-1973-0325507-9