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%I #19 Feb 11 2014 23:34:37
%S 1,4,112,144,23400,28224,247104,604800,26812800,2677752000,6805814400,
%T 165145780800,1248124550400,17996854730400,388778796252000
%N Indices of records in A171919 = number of solutions to n=x*y*z, x+y=z+1.
%C The sequence lists all n such that A171919(n) > A171919(k) for all k < n.
%C Also the subsequence of terms of A171920 for which A171919 is larger than for all preceding values.
%C The actual record values are given in A181486.
%C a(10) > 5*10^7.
%C It seems highly probable that all terms of this sequence, except for a(1) = 1, are multiples of 4.
%C a(14) > 4*10^12. - _Donovan Johnson_, Jun 14 2011
%C a(16) > 2*10^17. - _Robert Gerbicz_, Apr 10 2012
%e a(1) = 1 since there is no smaller value possible.
%e a(2) = 4 is the smallest number for which there are more than 1 = A171919(1) solutions to n = x*y*z, x + y = z + 1.
%e a(3) = 112 is the smallest number for which there are more than 2 = A171919(4) solutions to n = x*y*z, x + y = z + 1.
%o (PARI) m=0;for(n=1,1e9,A171919(n)>m | next; m=A171919(n); print1(n", "))
%K hard,more,nonn
%O 1,2
%A _R. J. Mathar_ and _M. F. Hasler_, Oct 23 2010
%E a(10)-a(13) from _Donovan Johnson_, Jun 14 2011
%E a(14)-a(15) from _Robert Gerbicz_, Apr 10 2012