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A290281
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Numbers k such that (k-1) mod phi(k) = lambda(k), where phi = A000010 and lambda = A002322.
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1
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6601, 11972017, 34657141, 67902031, 139952671, 258634741, 2000436751, 8801128801, 9116583841, 9462932431, 38069223721, 326170416001, 359316634951, 1860929324101, 2022188518351, 2283475947391, 2648686458601, 2697891108151, 4513362899761, 5020030521001, 5472940991761, 6163867710001, 7507903975951, 19288340548471
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OFFSET
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1,1
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COMMENTS
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Subsequence of the Carmichael numbers (A002997).
Composite numbers k such that (k-1) == lambda(k) (mod phi(k)).
Problem: are there infinitely many such numbers?
Conjecture: these are numbers k such that phi(k) + lambda(k) = k - 1. Checked up to 2^64. - Amiram Eldar and Thomas Ordowski, Dec 06 2019
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LINKS
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MAPLE
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count:= 0:
for cfile in ["carmichael-16", "carmichael17", "carmichael18"] do
do
S:= readline(cfile);
if S = 0 then break fi;
L:= map(parse, StringTools:-Split(S));
n:= L[1]; pm:= map(`-`, L[2..-1], 1);
phin:= convert(pm, `*`);
lambdan:= ilcm(op(pm));
if n-1 - lambdan mod phin = 0 then
count:= count+1; A[count]:= n;
fi
od:
fclose(cfile);
od:
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MATHEMATICA
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Select[Range[10^8], Divisible[# - 1, (lam = CarmichaelLambda[#])] && Mod[# - 1, EulerPhi[#]] == lam &] (* Amiram Eldar, Dec 06 2019 *)
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CROSSREFS
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KEYWORD
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nonn,changed
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AUTHOR
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STATUS
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approved
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