A097061 Carmichael numbers C such that C-1 is not a Niven/Harshad number.

561, 63973, 75361, 162401, 278545, 656601, 825265, 838201, 852841, 1050985, 1857241, 1909001, 3224065, 3828001, 4903921, 5444489, 5481451, 5632705, 5968873, 6049681, 6189121, 7995169, 8355841, 8830801, 8927101, 9494101, 9890881, 13696033, 14913991, 15247621, 17812081

Offset

1,1

Comments

8355841, 8830801, 8927101 are the first three consecutive Carmichael numbers to fail the criterion.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Andrew Granville and Carl Pomerance, Two contradictory conjectures concerning Carmichael numbers, Math. Comp. 71 (2002), pp. 883-908.

Rob Hoogers, Complete list of terms UP to 10^16 with all relevant data (5.3MB zipped textfile)

Example

Add all digits in 560 to get 11, which gives 560/11<>floor(560/11) and continue likewise with 1104/6==floor(1104/6), 1728/18==floor(1728/18), etc.

Mathematica

Select[Range[10^6], CompositeQ[#] && Divisible[# - 1, CarmichaelLambda[#]] && !Divisible[# - 1, Plus @@ IntegerDigits@(# - 1)] &] (* Amiram Eldar, Jun 24 2019 *)

Crossrefs

Cf. A002997, A005349.

Sequence in context: A006931 A258801 A329460 * A290497 A258839 A371759

Adjacent sequences: A097058 A097059 A097060 * A097062 A097063 A097064

Keyword

nonn,base

Author

Rob Hoogers (chimera(AT)chimera.fol.nl), Jul 21 2004

Extensions

Corrected by T. D. Noe, Nov 16 2006

Status

approved