A365337 The sum of divisors of the largest exponentially odd number dividing n.

1, 3, 4, 3, 6, 12, 8, 15, 4, 18, 12, 12, 14, 24, 24, 15, 18, 12, 20, 18, 32, 36, 24, 60, 6, 42, 40, 24, 30, 72, 32, 63, 48, 54, 48, 12, 38, 60, 56, 90, 42, 96, 44, 36, 24, 72, 48, 60, 8, 18, 72, 42, 54, 120, 72, 120, 80, 90, 60, 72, 62, 96, 32, 63, 84, 144, 68

Offset

1,2

Comments

The number of divisors of the largest exponentially odd number dividing n is A286324(n).

Links

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

Formula

a(n) = A000203(A350390(n)).

Multiplicative with a(p^e) = (p^(e+1)-1)/(p-1) if e is odd and (p^e-1)/(p-1) if e is even.

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

Sum_{k=1..n} a(k) ~ c * n^2 / 2, where c = Product_{p prime} (1 + 1/(p*(p^2-1))) = 1.2312911488886... (A065487). - Amiram Eldar, Sep 01 2023

Mathematica

f[p_, e_] := (p^(e + Mod[e, 2]) - 1)/(p - 1); a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100]

Prog

(PARI) a(n) = {my(f = factor(n)); prod(i = 1, #f~, (f[i, 1]^(f[i, 2] + f[i, 2]%2) - 1)/(f[i, 1] - 1)); }

Crossrefs

Cf. A000203, A065487, A286324, A350390.

Sequence in context: A069915 A033634 A366764 * A349337 A377604 A358045

Adjacent sequences: A365334 A365335 A365336 * A365338 A365339 A365340

Keyword

nonn,easy,mult

Author

Amiram Eldar, Sep 01 2023

Status

approved