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A006972 Lucas-Carmichael numbers: squarefree composite numbers n such that p | n => p+1 | n+1.
(Formerly M5450)
16
399, 935, 2015, 2915, 4991, 5719, 7055, 8855, 12719, 18095, 20705, 20999, 22847, 29315, 31535, 46079, 51359, 60059, 63503, 67199, 73535, 76751, 80189, 81719, 88559, 90287, 104663, 117215, 120581, 147455, 152279, 155819, 162687, 191807, 194327, 196559, 214199 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

REFERENCES

J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 399, p. 89, Ellipses, Paris 2008.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

Paolo P. Lava and Donovan Johnson, Table of n, a(n) for n = 1..10000 (first 550 terms from Paolo P. Lava)

Wikipedia, Lucas-Carmichael number

Index entries for sequences related to Carmichael numbers.

MATHEMATICA

Select[ Range[ 2, 10^6 ], !PrimeQ[ # ] && Union[ Transpose[ FactorInteger[ # ] ][ [ 2 ] ] ] == {1} && Union[ Mod[ # + 1, Transpose[ FactorInteger[ # ] ][ [ 1 ] ] + 1 ] ] == {0} & ]

PROG

(PARI) is(n)=my(f=factor(n)); for(i=1, #f[, 1], if((n+1)%(f[i, 1]+1) || f[i, 2]>1, return(0))); #f[, 1]>1 \\ Charles R Greathouse IV, Sep 23 2012

CROSSREFS

Intersection of A024556 and A056729.

Cf. A216925, A216926, A216927, A217002, A217003, A217091 (terms having 3, 4, 5, 6, 7 and 8 factors).

Sequence in context: A126231 A158317 A227008 * A216925 A206536 A065767

Adjacent sequences:  A006969 A006970 A006971 * A006973 A006974 A006975

KEYWORD

nonn

AUTHOR

rgep(AT)chalcedon.demon.co.uk; Jeffrey Shallit

STATUS

approved

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Last modified October 2 05:40 EDT 2014. Contains 247537 sequences.