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%I #15 Nov 29 2016 21:23:32
%S 1,3,4,5989,16
%N First term of maximal arithmetic progression with difference n, such that each term k has tau(k) = n.
%C a(6) <= 161804009483982959337354063701 if A165498(6) = 9, and at least 1e14.
%C a(8) = 380017309607.
%C a(10) <= 43920665884407841463671 if A165498(10) = 5 (found by _Giovanni Resta_), and at least 1e12.
%C a(12) <= 11673662470957217427690002629075 if A165498(12) = 10, and at least 1e10.
%C a(16) = 2a(8).
%C A165498(n) = 1 for odd n, so a(7) = 64; a(9) = 36; a(11) = 1024; a(13) = 4096; a(15) = 144; etc.
%e A165498(4) = 8, and exhaustive search finds tau(5989) = tau(5993) = tau(5997) = tau(6001) = tau(6005) = tau(6009) = tau(6013) = tau(6017) = 4 is the first example of an 8-term progression, so a(4) = 5989.
%Y Cf. A064491, A165497, A165498, A165501.
%K hard,nonn,more
%O 1,2
%A _Hugo van der Sanden_, Sep 21 2009; updated Nov 29 2016
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