A279254 Positive integers that have a record number of divisors in Gaussian integers.

1, 2, 4, 6, 8, 10, 20, 30, 40, 60, 100, 120, 180, 200, 240, 260, 300, 390, 520, 600, 780, 1200, 1300, 1560, 2340, 2600, 3120, 3900, 6630, 7800, 11700, 13260, 15600, 22100, 23400, 26520, 39780, 44200, 53040, 66300, 132600, 198900, 265200, 397800, 530400, 663000, 795600, 928200

Offset: 1

Author

J. Lowell, Dec 08 2016

Keywords

• nonn

Comments

Indices of records in A062327.

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..394

Crossrefs

Subsequence of A097752.

Cf. A062327, A002182 (factorization over the integers).

Programs

Mathematica

With[{s = Array[DivisorSigma[0, #, GaussianIntegers -> True] &, 10^6]}, Map[FirstPosition[s, #][[1]] &, Union@ FoldList[Max, s]]] (* Michael De Vlieger, Apr 05 2018 *)

PARI

b(n)= \\ A062327
{
    my(r=1,f=factor(n));
    for(j=1,#f[,1], my(p=f[j,1],e=f[j,2]);
        if(p==2,r*=(2*e+1));
        if(p%4==1,r*=(e+1)^2);
        if(p%4==3,r*=(e+1));
    );
    return(r);
}
{ my(r=0,t); for(n=1,10^6, t=b(n); if(t>r,r=t;print1(n,", "))); }
\\ Joerg Arndt, Dec 09 2016

Extensions

Terms a(11) and beyond from Joerg Arndt, Dec 09 2016