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%I #20 Oct 19 2020 12:35:47
%S 0,1,6,30,36,540,2100,3780,15120,37800,85680,120960,126000,131040,
%T 196560,302400,332640,786240,917280,1179360,2702700,3341520,4324320,
%U 8648640,19656000,19958400,21205800,43243200,46781280,57657600,64864800,122522400,151351200
%N Positions of records in A306440.
%C Numbers k such that A306440(k) > A306440(j) for all j < k.
%H Giovanni Resta, <a href="/A307221/b307221.txt">Table of n, a(n) for n = 1..50</a>
%e a(3) = 6 is in the sequence because A306440(6) = 2 while A306440(j) < 2 for 0 <= j < 6.
%p A306440:= proc(n) local t;
%p nops(select(t -> t^2<2*n and isprime(t+1) and isprime(2*n/t+1), numtheory:-divisors(2*n)))
%p end proc:
%p Res:= 0: vmax:= 0:
%p for n from 1 to 10^6 do
%p v:= A306440(n);
%p if v > vmax then
%p Res:= Res, n; vmax:= v;
%p fi
%p od:
%p Res;
%t A306440[n_] := Length[Select[Divisors[2n], #^2 < 2n && PrimeQ[#+1] && PrimeQ[2n/#+1]&]];
%t Res = {0}; vmax = 0;
%t For[n = 1, n <= 10^6 , n++, v = A306440[n]; If[v > vmax, Print[n]; AppendTo[Res, n]; vmax = v]];
%t Res (* _Jean-François Alcover_, Oct 17 2020, translated from Maple *)
%Y Cf. A306440.
%K nonn
%O 1,3
%A _Robert Israel_, Mar 29 2019
%E a(24)-a(33) from _Daniel Suteu_, Mar 29 2019
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