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%I #13 Apr 14 2021 01:17:59
%S 1,2,6,90,15120,983010
%N Positions of records in A343016.
%C Numbers k such that A343016(k) > A343016(j) for all j < k.
%C a(n) is divisible by 6 for n >= 3, by 30 for n >= 4, by 210 for n >= 5.
%C a(7) > 10^9 if it exists.
%e A343016(1) = 0.
%e A343016(2) = 1 is the first value > 0 in A343016.
%e A343016(6) = 5 is the first value > 1.
%e A343016(90) = 6 is the first value > 5.
%e A343016(15120) = 7 is the first value > 6.
%e A343016(983010) = 8 is the first value > 7.
%p R:= 1,2:
%p vmax:= 2:
%p f:= proc(n) local s, t, k;
%p s:= add(t[1]*t[2], t = ifactors(n)[2]);
%p for k from 0 do if not isprime(k*n+s) then return k fi od;
%p end proc:
%p for n from 6 by 6 to 10^6 do
%p v:= f(n);
%p if v > vmax then
%p vmax:= v;
%p R:= R, n;
%p fi
%p od:
%p R;
%t With[{s = Array[Block[{m = 0, k = Plus @@ Times @@@ FactorInteger[#]}, While[PrimeQ[# m + k], m++]; m] &, 10^6]}, Map[FirstPosition[s, #][[1]] &, Union@ FoldList[Max, s]]] (* _Michael De Vlieger_, Apr 13 2021 *)
%Y Cf. A343016.
%K nonn,more
%O 1,2
%A _J. M. Bergot_ and _Robert Israel_, Apr 02 2021
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