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A283656 Numbers n such that gcd(phi(n), n-1) > 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 (list; graph; refs; listen; history; text; internal format)
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 n-1 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 non-Carmichaels 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

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Last modified April 21 20:03 EDT 2019. Contains 322328 sequences. (Running on oeis4.)