cp's OEIS Frontend

A326312 Where the number of divisors d(k) reaches a new record for numbers k whose prime factors are of the form 3*j+2.

%I A326312 #17 Dec 23 2024 14:53:45
%S A326312 2,4,8,16,20,40,80,160,320,400,440,800,880,1600,1760,3520,4400,7040,
%T A326312 8800,14960,17600,29920,59840,74800,119680,149600,299200,598400,
%U A326312 1196800,1376320,1720400,2752640,3440800,6881600,13763200,27526400,34408000,49891600,68816000
%N A326312 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 A326312 Amiram Eldar, <a href="/A326312/b326312.txt">Table of n, a(n) for n = 1..300</a>
%H A326312 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 A326312 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 A326312 (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 A326312 divrecord=0;
%o A326312 for(k=2,50000000,my(j=pkn(k,3,2));if(j>divrecord,divrecord=j;print1(k,", ")))
%Y A326312 Cf. A053624, A071383, A230655, A326313, A326314.
%K A326312 nonn
%O A326312 1,1
%A A326312 _Hugo Pfoertner_, Sep 11 2019
%E A326312 More terms from _Amiram Eldar_, Sep 12 2019