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%I #17 May 05 2023 06:29:21
%S 561,63973,75361,162401,278545,656601,825265,838201,852841,1050985,
%T 1857241,1909001,3224065,3828001,4903921,5444489,5481451,5632705,
%U 5968873,6049681,6189121,7995169,8355841,8830801,8927101,9494101
%N Carmichael numbers C such that C-1 is not a Niven/Harshad number.
%C 8355841, 8830801, 8927101 are the first three consecutive Carmichael numbers to fail the criterion.
%H Amiram Eldar, <a href="/A097061/b097061.txt">Table of n, a(n) for n = 1..10000</a>
%H Andrew Granville and Carl Pomerance, <a href="http://dx.doi.org/10.1090/S0025-5718-01-01355-2">Two contradictory conjectures concerning Carmichael numbers</a>, Math. Comp. 71 (2002), pp. 883-90.
%H Rob Hoogers, <a href="http://aibots.myhost24.com/download/carmichael.zip">Complete list of terms UP to 10^16 with all relevant data (5.3MB zipped textfile)</a>
%e 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.
%t Select[Range[10^6], CompositeQ[#] && Divisible[# - 1, CarmichaelLambda[#]] && !Divisible[# - 1, Plus @@ IntegerDigits@(# - 1)] &] (* _Amiram Eldar_, Jun 24 2019 *)
%Y Cf. A002997, A005349.
%K nonn,base
%O 1,1
%A Rob Hoogers (chimera(AT)chimera.fol.nl), Jul 21 2004
%E Corrected by _T. D. Noe_, Nov 16 2006
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