A326312 - OEIS

%I #17 Dec 23 2024 14:53:45

%S 2,4,8,16,20,40,80,160,320,400,440,800,880,1600,1760,3520,4400,7040,

%T 8800,14960,17600,29920,59840,74800,119680,149600,299200,598400,

%U 1196800,1376320,1720400,2752640,3440800,6881600,13763200,27526400,34408000,49891600,68816000

%N Where the number of divisors d(k) reaches a new record for numbers k whose prime factors are of the form 3*j+2.

%H Amiram Eldar, <a href="/A326312/b326312.txt">Table of n, a(n) for n = 1..300</a>

%H Amiram Eldar, <a href="https://web.archive.org/web/*/http://list.seqfan.eu/oldermail/seqfan/2019-September/018904.html">A230655 & A071383 and (3, 1)- and (4, 1)-highly composite numbers</a>, thread in SeqFan mailing list, Sep 11 2019.

%t aQ[n_] := AllTrue[FactorInteger[n][[;; , 1]], Mod[#, 3] == 2 &]; 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,3,2));if(j>divrecord,divrecord=j;print1(k,", ")))

%Y Cf. A053624, A071383, A230655, A326313, A326314.

%K nonn

%O 1,1

%A _Hugo Pfoertner_, Sep 11 2019

%E More terms from _Amiram Eldar_, Sep 12 2019