Portal de Periódicos da CAPES

A search procedure and lower bound for odd perfect numbers

1973; American Mathematical Society; Volume: 27; Issue: 124 Linguagem: Inglês

10.1090/s0025-5718-1973-0325506-7

1088-6842

Bryant Tuckerman,

Machine Learning and Algorithms

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 {p^a} > {10^{18}} , with a even, or no divisor > 7 > 7 ; hence any opn must be > 10 36 > {10^{36}} .