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Numbers k such that k^2 + 1 is divisible by a 6th power.

2

`%I #13 Jul 04 2020 05:51:38
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`%S 1068,14557,16693,30182,32318,45807,47943,61432,63568,77057,79193,
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`%T 92682,94818,108307,110443,123932,126068,139557,141693,155182,157318,
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`%U 170807,172943,186432,188568,202057,204193,217682,219818,233307,235443,248932,251068,264557
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`%N Numbers k such that k^2 + 1 is divisible by a 6th power.
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`%H Amiram Eldar, <a href="/A218565/b218565.txt">Table of n, a(n) for n = 1..10000</a>
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`%e 1068 is in the sequence because 1068^2 + 1 = 5^6 * 73.
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`%e 390112 is in the sequence because 390112^2 + 1 = 5 * 13 * 17 ^ 6 * 97.
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`%e 1999509 is in the sequence because 1999509^2 + 1 = 2 * 13 ^ 6 * 29 * 14281.
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`%t Select[Range[2,27000],Max[Transpose[FactorInteger[#^2+1]][[2]]]>5&]
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`%Y Cf. A002522, A049532, A034939, A218562, A218563, A218564.
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`%Y Cf. A001014 (6th powers).
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`%K nonn
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`%O 1,1
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`%A _Michel Lagneau_, Nov 02 2012
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