

A283656


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


1



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

Table of n, a(n) for n=1..50.


CROSSREFS

Cf. A000010, A002322, A002997, A049559, A264012.
Sequence in context: A250642 A280755 A020140 * A020194 A094447 A020224
Adjacent sequences: A283653 A283654 A283655 * A283657 A283658 A283659


KEYWORD

nonn


AUTHOR

Thomas Ordowski and Altug Alkan, Mar 23 2017


STATUS

approved



