A302249 a(n) is the number of divisors of A279254(n) in Gaussian integers.

1, 3, 5, 6, 7, 12, 20, 24, 28, 40, 45, 56, 60, 63, 72, 80, 90, 96, 112, 126, 160, 162, 180, 224, 240, 252, 288, 360, 384, 504, 540, 640, 648, 720, 756, 896, 960, 1008, 1152, 1440, 2016, 2160, 2592, 3024, 3168, 3584, 3888, 4032

Offset: 1

Author

Jianing Song, Apr 04 2018

Keywords

• nonn

Comments

The divisors are counted mod associates.

Conjecture: a(14) = 63 is the largest odd term.

Examples

			A279254(14) = 200 and 200 has 63 divisors in Gaussian integers (up to association), so a(14) = 63.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..394 (calculated from the b-file at A279254)
• Index entries for Gaussian integers and primes

Crossrefs

Cf. A062327, A279254.

Programs

Mathematica

With[{s = Array[DivisorSigma[0, #, GaussianIntegers -> True] &, 10^6]}, 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(t, ", "))); }
\\ Joerg Arndt, Apr 04 2018

Formula

a(n) = A062327(A279254(n)).