A324184 a(n) = sigma(A163511(n)).

1, 3, 7, 4, 15, 13, 12, 6, 31, 40, 39, 31, 28, 24, 18, 8, 63, 121, 120, 156, 91, 124, 93, 57, 60, 78, 72, 48, 42, 32, 24, 12, 127, 364, 363, 781, 280, 624, 468, 400, 195, 403, 372, 342, 217, 228, 171, 133, 124, 240, 234, 248, 168, 192, 144, 96, 90, 104, 96, 72, 56, 48, 36, 14, 255, 1093, 1092, 3906, 847, 3124, 2343, 2801, 600

Offset: 0

Author

Antti Karttunen, Feb 17 2019

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 0..16383
• Antti Karttunen, Data supplement: n, a(n) computed for n = 0..65537

Crossrefs

Cf. A000203, A054429, A163511, A324054, A324183, A324185, A324186, A324187, A324188, A324189.

Programs

PARI

A324184(n) = if(!n,1,my(p=2,mp=p*p,m=1); while(n>1, if(n%2, p=nextprime(1+p); mp = p*p, if((2==n)||!(n%4),mp *= p,m *= (mp-1)/(p-1))); n >>= 1); (m*(mp-1)/(p-1)));

PARI

A163511(n) = if(!n,1,my(p=2, t=1); while(n>1, if(!(n%2), (t*=p), p=nextprime(p+1)); n >>= 1); (t*p));
A324184(n) = sigma(A163511(n));

Python

from sympy import nextprime
def A324184(n):
    if n:
        c, p = 1, 1
        while n:
            c *= ((p:=nextprime(p))**(s:=(~n&n-1).bit_length()+1)-1)//(p-1)
            n >>= s
        return c*(p**(s+1)-1)//(p**s-1)
    return 1 # Chai Wah Wu, Jul 25 2023

Formula

a(n) = A000203(A163511(n)).

For n >= 1, a(n) = A324054(A054429(n)).