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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.
3
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, 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
KEYWORD
nonn
AUTHOR
Hugo Pfoertner, Sep 11 2019
EXTENSIONS
More terms from Amiram Eldar, Sep 12 2019
STATUS
approved