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A178705 Odd composite numbers q such that there exists a, 2<=a<=q-2, such that a^d == 1 mod q where d = A000265(q-1). Thus q is a strong pseudoprime in base a. 1
49, 91, 121, 133, 169, 175, 217, 231, 247, 259, 301, 325, 341, 343, 361, 385, 403, 427, 435, 451, 469, 475, 481, 511, 529, 553, 559, 561, 589, 595, 637, 645, 651, 671, 679, 703, 715, 721, 763, 775, 781, 793, 805, 817, 841, 847, 861, 871, 889, 891, 925, 931, 949, 961, 973, 1001, 1015, 1027, 1035, 1045 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Odd composite numbers q such that gcd(A000010(q), A000265(q-1)) > 1. - Robert Israel, Dec 20 2017

LINKS

Robert Israel, Table of n, a(n) for n = 1..10000

FORMULA

a^d == 1 mod q

EXAMPLE

18^3 == 1 mod 49

MAPLE

filter:= proc(n)

  if isprime(n) then return false fi;

  igcd((n-1)/2^padic:-ordp(n-1, 2), numtheory:-phi(n)) > 1

end proc:

select(filter, [seq(i, i=9..2000, 2)]); # Robert Israel, Dec 20 2017

MATHEMATICA

filterQ[n_] := If[PrimeQ[n], False, GCD[(n-1)/2^IntegerExponent[n-1, 2], EulerPhi[n]] > 1];

Select[Range[9, 2000, 2], filterQ] (* Jean-Fran├žois Alcover, Sep 25 2020, after Robert Israel *)

CROSSREFS

Cf. A000010, A000265.

Sequence in context: A350704 A157342 A230226 * A118886 A198773 A320633

Adjacent sequences:  A178702 A178703 A178704 * A178706 A178707 A178708

KEYWORD

nonn

AUTHOR

Karsten Meyer, Dec 26 2010

EXTENSIONS

Corrected by Robert Israel, Dec 20 2017

STATUS

approved

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Last modified August 15 02:47 EDT 2022. Contains 356122 sequences. (Running on oeis4.)