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A290281 Numbers n such that (n-1) mod phi(n) = lambda(n), where phi = A000010 and lambda = A002322. 1
6601, 11972017, 34657141, 67902031, 139952671, 258634741, 2000436751, 8801128801, 9116583841, 9462932431, 38069223721, 326170416001, 359316634951, 1860929324101, 2022188518351, 2283475947391, 2648686458601, 2697891108151, 4513362899761, 5020030521001, 5472940991761, 6163867710001, 7507903975951, 19288340548471 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Numbers n such that A215486(n) = A002322(n).

Subset of the Carmichael numbers (A002997).

Composite numbers n such that (n-1) == lambda(n) (mod phi(n)).

Composite numbers n such that A277127(n) == 1 (mod A000010(n)).

Problem: are there infinitely many such numbers?

LINKS

Robert Israel, Table of n, a(n) for n = 1..79

MAPLE

# Using data files for A002997

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:

seq(A[i], i=1..count); # Robert Israel, Jul 26 2017

CROSSREFS

Cf. A000010, A002322, A002997, A215486.

Subsequence of A264012.

Sequence in context: A164971 A214434 A317247 * A178213 A237320 A237726

Adjacent sequences:  A290278 A290279 A290280 * A290282 A290283 A290284

KEYWORD

nonn

AUTHOR

Robert Israel and Thomas Ordowski, Jul 25 2017

STATUS

approved

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Last modified April 19 10:39 EDT 2019. Contains 322255 sequences. (Running on oeis4.)