%I #18 Sep 12 2019 11:49:09
%S 3,9,21,63,189,441,567,693,2079,4851,6237,13167,39501,92169,118503,
%T 276507,829521,908523,2119887,2725569,6359661,19078983,28164213,
%U 57236949,84492639,171710847,197149491,591448473,1211061159,1774345419,3633183477,5323036257,6505933203
%N Where the number of divisors d(k) reaches a new record for numbers k whose prime factors are of the form 4*j+3.
%C For references and links see A326312.
%H Amiram Eldar, <a href="/A326313/b326313.txt">Table of n, a(n) for n = 1..300</a>
%t aQ[n_] := AllTrue[FactorInteger[n][[;; , 1]], Mod[#, 4] == 3 &]; s[n_] := DivisorSum[n, 1 &, aQ[#] &]; sm = 0; seq = {}; Do[s1 = s[n]; If[s1 > sm, sm = s1; AppendTo[seq, n]], {n, 2, 10^5}]; seq (* _Amiram Eldar_, Sep 12 2019 *)
%o (PARI) pkn(x,d,m)={my(fn=factor(x),nf=#fn[,1]);for(k=1,nf,if(fn[k,1]%d!=m,return(0)));numdiv(x)};
%o divrecord=0;
%o for(k=2,50000000,my(j=pkn(k,4,3));if(j>divrecord,divrecord=j;print1(k,", ")))
%Y Cf. A053624, A071383, A230655, A326312, A326314.
%K nonn
%O 1,1
%A _Hugo Pfoertner_, Sep 11 2019
%E More terms from _Amiram Eldar_, Sep 12 2019