Numbers 410,000s

A page of the Numeropedia - the Special Encyclopedia of Numbers

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410,041

[Math.]  A Carmichael number: 410,041 = 41×73×137. Number 41041 is also a Carmichael number.

 

410,256

[Math.]  102,564×4 = 410,256.

 

413,475

[Math.]   Two consecutive sums of consecutive numbers:

5476+…+5550 = 5551+…+5624 = 413,475.

 

413,908

[Math.]  127,194,229,449 = (127194+229449)2 = 356,6432 and

413,908,229,449 = (413908+229449)2 = 643,3572 and 356,643+643357 = 1,000,000.

 

414,560

[Math.]   4424814 = 4145604+2175194+958004. The smallest counter-example to disprove Euler’s conjecture that it always requires at least n terms (of nth power) to sum to an nth power, nontrivially. (Fermat’s Last Theorem is a special case for only 2 terms).

 

415,278

[Math.]  172,455,817,284 = 415,2782, each digit is duplicated.

 

418,904  

[Math.]  The 2nd known amicable/sociable number chain: 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. (of 28 links, currently the longest, found by Poulet, 1918)