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
Keywords
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.
Programs
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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)];
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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
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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 *)