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.

2, 4, 8, 16, 20, 40, 80, 160, 320, 400, 440, 800, 880, 1600, 1760, 3520, 4400, 7040, 8800, 14960, 17600, 29920, 59840, 74800, 119680, 149600, 299200, 598400, 1196800, 1376320, 1720400, 2752640, 3440800, 6881600, 13763200, 27526400, 34408000, 49891600, 68816000

Offset

1,1

Links

Amiram Eldar, Table of n, a(n) for n = 1..300

Amiram Eldar, A230655 & A071383 and (3, 1)- and (4, 1)-highly composite numbers, thread in SeqFan mailing list, Sep 11 2019.

Mathematica

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 *)

Prog

(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)};
divrecord=0;
for(k=2, 50000000, my(j=pkn(k, 3, 2)); if(j>divrecord, divrecord=j; print1(k, ", ")))

Crossrefs

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

Sequence in context: A166156 A089473 A118021 * A134162 A244484 A350414

Adjacent sequences: A326309 A326310 A326311 * A326313 A326314 A326315

Keyword

nonn

Author

Hugo Pfoertner, Sep 11 2019

Extensions

More terms from Amiram Eldar, Sep 12 2019

Status

approved