A326314 - OEIS

%I #17 Sep 12 2019 11:57:37

%S 5,25,55,275,935,3025,4675,21505,51425,107525,537625,1182775,2688125,

%T 3118225,15591125,34300475,77955625,127847225,583108075,639236125,

%U 1406319475,3196180625,6008819575,23907431075,30044097875,66097015325,150220489375,318467437475,1123649260525

%N Where the number of divisors d(k) reaches a new record for numbers k whose prime factors are of the form 6*j+5.

%C For references and links see A326312.

%H Amiram Eldar, <a href="/A326314/b326314.txt">Table of n, a(n) for n = 1..300</a>

%t aQ[n_] := AllTrue[FactorInteger[n][[;; , 1]], Mod[#, 6] == 5 &]; 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, 200000000, my(j=pkn(k, 6, 5)); if(j>divrecord, divrecord=j; print1(k, ", ")))

%Y Cf. A053624, A071383, A230655, A326312, A326313.

%K nonn

%O 1,1

%A _Hugo Pfoertner_, Sep 11 2019

%E More terms from _Amiram Eldar_, Sep 12 2019