Paul Poulet


Paul Poulet was a self-taught Belgian mathematician who made several important contributions to number theory, including the discovery of sociable numbers in 1918. He is also remembered for calculating the pseudoprimes to base two, first up to 50 million in 1926, then up to 100 million in 1938. These are now often called Poulet numbers in his honour. In 1925, he published forty-three new multiperfect numbers, including the first two known octo-perfect numbers. His achievements are particularly remarkable given that he worked without the aid of modern computers and calculators.

Career

Poulet published at least two books about his mathematical work, Parfaits, amiables et extensions and La chasse aux nombres . He wrote the latter in the French village of Lambres-lez-Aire in the Pas-de-Calais, a short distance across the border with Belgium. Both were published by éditions Stevens of Brussels.

Sociable chains

In a sociable chain, or aliquot cycle, a sequence of divisor-sums returns to the initial number. These are the two chains Poulet described in 1918:
12496 → 14288 → 15472 → 14536 → 14264 → 12496
14316 → 19116 → 31704 → 47616 → 83328 → 177792 → 295488 → 629072 → 589786 → 294896 → 358336 → 418904 → 366556 → 274924 → 275444 → 243760 → 376736 → 381028 → 285778 → 152990 → 122410 → 97946 → 48976 → 45946 → 22976 → 22744 → 19916 → 17716 → 14316
The second chain remains by far the longest known, despite the exhaustive computer searches begun by the French mathematician Henri Cohen in 1969. Poulet introduced sociable chains in a paper in the journal L'Intermédiaire des Mathématiciens #25. The paper ran like this:
The French original runs like this: