A377517 The sum of the divisors of n that are terms in A276078.

1, 3, 4, 3, 6, 12, 8, 3, 13, 18, 12, 12, 14, 24, 24, 3, 18, 39, 20, 18, 32, 36, 24, 12, 31, 42, 13, 24, 30, 72, 32, 3, 48, 54, 48, 39, 38, 60, 56, 18, 42, 96, 44, 36, 78, 72, 48, 12, 57, 93, 72, 42, 54, 39, 72, 24, 80, 90, 60, 72, 62, 96, 104, 3, 84, 144, 68, 54

Offset

1,2

Comments

First differs from A046897 at n = 27 = 3^3: a(27) = 13, while A046897(27) = 40.

The number of these divisors is A377516(n), and the largest of them is A377515(n).

Links

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

Formula

a(n) = A000203(A377515(n)).

Multiplicative with a(p^e) = (p^(min(pi(p), e)+1) - 1)/(p - 1), where pi(n) = A000720(n).

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

Sum_{k=1..n} a(k) ~ c * n^2 / 2, where c = zeta(2) * Product_{p prime} (1 - 1/p^(pi(p)+1)) = 1.18603586369737251334... .

Mathematica

f[p_, e_] := (p^(Min[PrimePi[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)); prod(i = 1, #f~, (f[i, 1]^(min(primepi(f[i, 1]), f[i, 2]) + 1) - 1)/(f[i, 1] - 1)); }

Crossrefs

Cf. A000203, A000720, A013661, A046897, A276078, A377515, A377516, A377520.

Sequence in context: A073181 A183100 A340323 * A046897 A109506 A369889

Adjacent sequences: A377514 A377515 A377516 * A377518 A377519 A377520

Keyword

nonn,easy,mult

Author

Amiram Eldar, Oct 30 2024

Status

approved