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

1,4

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

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

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 *)

Prog

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

Crossrefs

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

Cf. A047994, A173557.

Sequence in context: A360288 A263756 A204984 * A243473 A325969 A325826

Adjacent sequences: A335338 A335339 A335340 * A335342 A335343 A335344

Keyword

nonn,mult,easy

Author

R. J. Mathar, Jun 02 2020

Status

approved