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A074379 Super-Carmichael numbers with exactly 4 factors. 8
41041, 62745, 63973, 75361, 101101, 126217, 172081, 188461, 278545, 340561, 449065, 552721, 656601, 658801, 670033, 748657, 838201, 852841, 997633, 1033669, 1082809, 1569457, 1773289, 2100901, 2113921, 2433601, 2455921 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Super-Carmichael numbers are Carmichael numbers (A002997) for which Moebius function mu(n) is 1 (A008683). There are no super-Carmichael numbers with exactly 2 factors since Carmichael numbers must have at least 3 factors.

LINKS

R. J. Mathar, Table of n, a(n) for n = 1..6042

EXAMPLE

41041 = 7 * 11 * 13 * 41, 62745 = 3 * 5 * 47 * 89, ...

MATHEMATICA

p = Table[ Prime[i], {i, 1, 10}]; f[n_] := Union[ PowerMod[ Select[p, GCD[ #, n] == 1 & ], n - 1, n]]; Select[ Range[2500000], !PrimeQ[ # ] && OddQ[ # ] && Length[ FactorInteger[ # ]] == 4 && MoebiusMu[ # ] == 1 && f[ # ] == {1} & ]

CROSSREFS

Cf. A002997, A006931.

Sequence in context: A173361 A047828 A141711 * A237395 A252121 A252118

Adjacent sequences:  A074376 A074377 A074378 * A074380 A074381 A074382

KEYWORD

nonn

AUTHOR

Jani Melik, Sep 24 2002

EXTENSIONS

Edited and extended by Robert G. Wilson v, Oct 03 2002

STATUS

approved

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Last modified December 3 18:47 EST 2016. Contains 278745 sequences.