A221743 Numbers k such that (6*k+1)*(12*k+1)*(18*k+1) is a Carmichael number which is the product of four prime numbers.

5, 11, 15, 61, 85, 115, 455, 661, 700, 805, 920, 1225, 1326, 1910, 2961, 4935, 5425, 6565, 8175, 10885, 11375, 12155, 13230, 18315, 37800, 39325, 45325, 59726, 69440, 99645, 113120, 121365, 129850, 144685, 211945, 353465, 378940, 389896, 392625

Offset

1,1

Links

Amiram Eldar, Table of n, a(n) for n = 1..500

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(n); fi;
fi; od; end: P(10^6); # Paolo P. Lava, Oct 11 2013

Mathematica

IsCarmichaelQ[n_] := Module[{f}, If[EvenQ[n] || PrimeQ[n], False, f = Transpose[FactorInteger[n]][[1]]; Union[Mod[n-1, f-1]] == {0}]]; n = 0; t = {}; While[Length[t] < 39, n++; c = (6*n + 1)*(12*n + 1)*(18*n + 1); If[SquareFreeQ[c] && Length[FactorInteger[c]] == 4 && IsCarmichaelQ[c], AppendTo[t, n]]]; t (* T. D. Noe, Jan 23 2013 *)

Prog

(Magma) [n: n in [1..4*10^5] | #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, A221742 (associated Carmichael numbers).

Subsequence of A101187.

Sequence in context: A136975 A136973 A276037 * A137008 A137010 A137007

Adjacent sequences: A221740 A221741 A221742 * A221744 A221745 A221746

Keyword

nonn

Author

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

Status

approved