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%I #6 Jan 16 2015 09:24:03
%S 16,17,33,34,50,51,84,119,135,153,169,220,255,272,288,374,441,560,594,
%T 714,832,935,1088,1155,1224,1274,1700,2057,2430,2499,2600,4913,5831,
%U 12375,14399,28560,31212,37179,194480,336140
%N The largest prime factor of n*(n+1) equals 17. (Related to the abc conjecture.)
%C Equivalently, the prime factors of n and n+1 are not larger than 17, but not all smaller than 17 (in which case n is in A252493).
%C This sequence is complete by a theorem of Stormer, cf. A002071 and sequences A085152, A085153, A252494, A252493.
%C This is row 7 of A145605. It has A145604(7)=40 terms and ends with A002072(7)=336140.
%H <a href="/index/Ab#abc">OEIS Index entries for sequences related to the abc conjecture</a>
%t Select[Range[345678], FactorInteger[ # (# + 1)][[ -1,1]] == 17 &]
%o (PARI) for(n=1,9e6,vecmax(factor(n++)[,1])<18 && vecmax(factor(n*n--)[,1])==17 && print1(n",")) \\ Skips 2 if n+1 is not 17-smooth: Twice as fast as the naïve version.
%Y Cf. A002473, A086247, A252493, A252494, A085153, A085152.
%K nonn,fini,full
%O 1,1
%A _M. F. Hasler_, Jan 16 2015
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