A221742 Carmichael numbers of the form (6*k+1)*(12*k+1)*(18*k+1) which are the product of four prime numbers.

172081, 1773289, 4463641, 295643089, 798770161, 1976295241, 122160500281, 374464040689, 444722065201, 676328168881, 1009514855521, 2382986541601, 3022286597929, 9031805532361, 33648448111489, 155773422536761, 206932492972801, 366715617643441, 708083570971801

Offset

1,1

Links

Amiram Eldar, Table of n, a(n) for n = 1..500 (terms 1..87 from Vincenzo Librandi)

Umberto Cerruti, Pseudoprimi di Fermat e numeri di Carmichael (in Italian), 2013. The sequence is on page 11.

Index entries for sequences related to Carmichael numbers.

Maple

with(numtheory); P:=proc(q)local a, b, k, ok, n;
for n from 0 to q do a:=(6*n+1)*(12*n+1)*(18*n+1); b:=ifactors(a)[2];
if issqrfree(a) and nops(b)=4 then ok:=1;
for k from 1 to 4 do if not type((a-1)/(b[k][1]-1), integer) then ok:=0;
break; fi; od; if ok=1 then print(a); fi;
fi; od; end: P(10^6); # Paolo P. Lava, Oct 11 2013

Mathematica

g[n_] := (6*n+1)*(12*n+1)*(18*n+1); testQ[n_] := Block[{p, e}, {p, e} = Transpose@ FactorInteger@ n; e == {1, 1, 1, 1} && Max[Mod[n-1, p-1]] == 0]; Select[g /@ Range[10^4], testQ] (* Giovanni Resta, May 21 2013 *)

Prog

(Magma) [c: n in [1..10^4] | #PrimeDivisors(c) eq 4 and IsOne(c mod CarmichaelLambda(c)) where c is (6*n+1)*(12*n+1)*(18*n+1)];

Crossrefs

Cf. A002997, A033502, A221743 (associated k).

Subsequence of A182087.

Sequence in context: A376503 A049053 A242980 * A239789 A233488 A233483

Adjacent sequences: A221739 A221740 A221741 * A221743 A221744 A221745

Keyword

nonn

Author

Bruno Berselli, Jan 23 2013, based on the Cerruti paper.

Status

approved