

A283656


Numbers n such that gcd(phi(n), n1) > lambda(n).


3



65, 91, 217, 273, 451, 481, 703, 793, 1281, 1729, 1891, 1921, 2465, 2701, 3201, 4033, 4097, 4681, 5833, 6643, 6697, 7105, 7161, 8321, 8401, 8911, 9073, 10649, 11041, 11476, 11521, 12403, 12545, 13051, 14689, 14701, 15841, 16385, 16401, 16471, 18361, 18705, 18721, 19684, 19951, 20801, 21953, 22177, 22681, 23001
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OFFSET

1,1


COMMENTS

All terms are composite. No powers of primes.
Contains all Carmichael numbers except A264012.
If n is in the sequence, then n1 is not squarefree.
Problem: are there infinitely many such even numbers? : 11476, 19684, 24564, 37576, 57226, 65026, 80476, 89776, 91356, ...
It is possible to show there are infinitely many Carmichael numbers with the property. In fact this follows with a small modification of the original proof of the infinitude of the Carmichael numbers. It seems harder though to prove that there are infinitely many nonCarmichaels with the property, though undoubtedly it's true.  Carl Pomerance, Mar 24 2017


LINKS



MATHEMATICA

Select[Range[10^4], GCD[EulerPhi[#], #1] > CarmichaelLambda[#] &] (* Amiram Eldar, Aug 26 2019 *)


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



