

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.


2



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
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OFFSET

1,1


LINKS

Table of n, a(n) for n=1..39.
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((a1)/(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[n1, f1]] == {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



