A326313 -id:A326313 - 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.

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

Hugo Pfoertner, Sep 11 2019

nonn

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.

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

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 *)

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,", ")))

More terms from Amiram Eldar, Sep 12 2019

A326314 Where the number of divisors d(k) reaches a new record for numbers k whose prime factors are of the form 6*j+5.

Original entry on oeis.org

5, 25, 55, 275, 935, 3025, 4675, 21505, 51425, 107525, 537625, 1182775, 2688125, 3118225, 15591125, 34300475, 77955625, 127847225, 583108075, 639236125, 1406319475, 3196180625, 6008819575, 23907431075, 30044097875, 66097015325, 150220489375, 318467437475, 1123649260525

Offset: 1

Hugo Pfoertner, Sep 11 2019

nonn

For references and links see A326312.

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

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

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 *)

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, 200000000, my(j=pkn(k, 6, 5)); if(j>divrecord, divrecord=j; print1(k, ", ")))

More terms from Amiram Eldar, Sep 12 2019

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.

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