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

Offset: 1

Author

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

Keywords

• nonn
• base

Comments

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

Examples

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

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. 883-90.
• Rob Hoogers, Complete list of terms UP to 10^16 with all relevant data (5.3MB zipped textfile)

Crossrefs

Cf. A002997, A005349.

Programs

Mathematica

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

Extensions

Corrected by T. D. Noe, Nov 16 2006