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单词 SuperPouletNumber
释义

super-Poulet number


A super-Poulet numberMathworldPlanetmath n is a Poulet numberMathworldPlanetmath which besides satisfying the congruenceMathworldPlanetmathPlanetmathPlanetmath 2n2modn, each of its divisorsMathworldPlanetmathPlanetmath di (for 1<iτ(n)) also satisfies the congruence 2di2moddi.

Two examples: 341 is a super-Poulet number, with its divisors being 1, 11, 31 and 341 itself. We verify that 211=2048=11×186+2 and 231=2147483648=31×69273666+2. 341 itself has already been checked when confirmed as a Poulet number. Now, 561 is a Poulet number but not a super-Poulet number since one of its divisors, 33, does not satisfy the congruence: 233-233260301048.18181818.

The first few super-Poulet numbers are 341, 1387, 2047, 2701, 3277, 4033, 4369, 4681, 5461, 7957, 8321, which are listed in A050217 of Sloane’s OEIS.

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更新时间:2025/5/4 22:42:15