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Mathematics of Computation

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A search procedure and lower bound for odd perfect numbers


Author: Bryant Tuckerman
Journal: Math. Comp. 27 (1973), 943-949
MSC: Primary 10A25; Secondary 10-04
Corrigendum: Math. Comp. 28 (1974), 887.
Corrigendum: Math. Comp. 28 (1974), 887.
MathSciNet review: 0325506
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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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DOI: https://doi.org/10.1090/S0025-5718-1973-0325506-7
Keywords: Odd perfect numbers, perfect numbers
Article copyright: © Copyright 1973 American Mathematical Society