Примитивное полусовершенное число

Примитивное полусовершенное число — полусовершенное число, среди собственных делителей которого нет других полусовершенных чисел. Поскольку любое число, кратное полусовершенному, само является полусовершенным, любое примитивное полусовершенное число порождает бесконечное множество полусовершенных чисел, кратных , из которых только само является примитивным.

Первые полусовершенные числа[1]:

6, 20, 28, 88, 104, 272, 304, 350, 368, 464, 490, 496, 550, 572, 650, 748, 770, 910, 945, …

Большинство примитивных полусовершенных чисел являются чётными: первое нечётное число — 945, однако установлено, что нечётных примитивных полусовершенных чисел также бесконечно много.

Примечания

  1. ↑ последовательность A006036 в OEIS

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