A335341 Sum of divisors of A003557(n).

1, 1, 1, 3, 1, 1, 1, 7, 4, 1, 1, 3, 1, 1, 1, 15, 1, 4, 1, 3, 1, 1, 1, 7, 6, 1, 13, 3, 1, 1, 1, 31, 1, 1, 1, 12, 1, 1, 1, 7, 1, 1, 1, 3, 4, 1, 1, 15, 8, 6, 1, 3, 1, 13, 1, 7, 1, 1, 1, 3, 1, 1, 4, 63, 1, 1, 1, 3, 1, 1, 1, 28, 1, 1, 6, 3, 1, 1, 1

Offset: 1

Author

R. J. Mathar, Jun 02 2020

Keywords

• nonn
• mult
• easy

Comments

The sum of the divisors d of n such that n/d is a coreful divisor of n (a coreful divisor of n is a divisor with the same squarefree kernel as n). The number of these divisors is A005361(n). - Amiram Eldar, Jun 30 2023

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16383
• Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537

Crossrefs

Cf. A000203, A003557, A005361 (number of divisors of A003557), A336567.

Cf. A047994, A173557.

Programs

Maple

A335341 := proc(n)
    local a,pe,p,e ;
    a := 1;
    for pe in ifactors(n)[2] do
        p := op(1,pe) ;
        e := op(2,pe) ;
        if e > 1 then
            a := a*(p^e-1)/(p-1) ;
        end if;
    end do:
    a ;
end proc:

Mathematica

f[p_, e_] := (p^e-1)/(p-1); a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Sep 26 2020 *)

PARI

a(n) = sigma(n/factorback(factor(n)[, 1])); \\ Michel Marcus, Jun 02 2020

Formula

a(n) = A000203(A003557(n)).

Multiplicative with a(p^1)=1 and a(p^e) = (p^e-1)/(p-1) if e>1.

A057723(n) = A007947(n)*a(n).

a(n) = 1 iff n in A005117.

a(n) = A336567(n) + A003557(n). - Antti Karttunen, Jul 28 2020

Dirichlet g.f.: zeta(s-1) * zeta(s) * Product_{p prime} (1 - 1/p^(s-1) + 1/p^(2*s-1)). - Amiram Eldar, Sep 09 2023

a(n) = A047994(n)/A173557(n). - Ridouane Oudra, Oct 30 2023