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A306338
Carmichael numbers k such that phi(k) divides (k-1)*lambda(k).
1
561, 1105, 1729, 2465, 6601, 15841, 41041, 46657, 52633, 75361, 115921, 334153, 340561, 658801, 670033, 2455921, 2704801, 4903921, 5049001, 6049681, 6840001, 8355841, 9439201, 9582145, 9613297, 10402561, 11119105, 11205601, 11972017, 14469841, 15888313, 16778881
OFFSET
1,1
COMMENTS
Carmichael numbers k such that A034380(k) divides k-1.
A proper subset of Carmichael numbers in A173703.
The number of terms below 10^k for k=1,2,...,18 is 0, 0, 1, 5, 10, 15, 25, 56, 101, 184, 310, 508, 814, 1265, 1964, 2990, 4486, 6704. Cf. A055553.
Composite numbers k such that lcm(lambda(k),phi(k)/lambda(k)) divides k-1.
Problem: are there infinitely many such numbers?
MATHEMATICA
Select[Range[3, 100000, 2], !PrimeQ[#] && Divisible[#-1, c = CarmichaelLambda[#]] && Divisible[c*(#-1), EulerPhi[#]] &]
CROSSREFS
KEYWORD
nonn
AUTHOR
Amiram Eldar and Thomas Ordowski, Feb 08 2019
STATUS
approved