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
Keywords
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.
Programs
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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)];
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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(a); fi; fi; od; end: P(10^6); # Paolo P. Lava, Oct 11 2013
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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 *)