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

1,2

Comments

Indices of records in A062327.

Links

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

Mathematica

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

Prog

(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

Crossrefs

Subsequence of A097752.

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

Sequence in context: A373574 A157006 A221991 * A373402 A212495 A083490

Adjacent sequences: A279251 A279252 A279253 * A279255 A279256 A279257

Keyword

nonn

Author

J. Lowell, Dec 08 2016

Extensions

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

Status

approved