A366146 The sum of divisors of the largest divisor of n that is a cubefull number (A036966).

1, 1, 1, 1, 1, 1, 1, 15, 1, 1, 1, 1, 1, 1, 1, 31, 1, 1, 1, 1, 1, 1, 1, 15, 1, 1, 40, 1, 1, 1, 1, 63, 1, 1, 1, 1, 1, 1, 1, 15, 1, 1, 1, 1, 1, 1, 1, 31, 1, 1, 1, 1, 1, 40, 1, 15, 1, 1, 1, 1, 1, 1, 1, 127, 1, 1, 1, 1, 1, 1, 1, 15, 1, 1, 1, 1, 1, 1, 1, 31, 121, 1

Offset

1,8

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Formula

a(n) = A000203(A360540(n)).

a(n) = A000203(n)/A366148(n).

a(n) >= 1, with equality if and only if n is cubefree (A004709).

a(n) <= A000203(n), with equality if and only if n is cubefull (A036966).

Multiplicative with a(p^e) = 1 if e <= 2 and (p^(e+1)-1)/(p-1) otherwise.

Dirichlet g.f.: zeta(s-1) * zeta(s) * Product_{p prime} (1 - 1/p^(s-1) + 1/p^(3*s-3) + 1/p^(3*s-2) + 1/p^(3*s-1) - 1/p^(4*s-3) - 1/p^(4*s-2)).

Mathematica

f[p_, e_] := If[e < 3, 1, (p^(e+1)-1)/(p-1)]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100]

Prog

(PARI) a(n) = {my(f = factor(n), p = f[, 1], e = f[, 2]); prod(i = 1, #p, if(e[i] < 3, 1, (p[i]^(e[i]+1)-1)/(p[i]-1)))};

Crossrefs

Cf. A000203, A036966, A295294, A360540, A366076, A366145, A366148.

Sequence in context: A333845 A015908 A361355 * A040228 A040229 A318650

Adjacent sequences: A366143 A366144 A366145 * A366147 A366148 A366149

Keyword

nonn,easy,mult

Author

Amiram Eldar, Oct 01 2023

Status

approved