A377520 The sum of the divisors of n that are terms in A207481.

1, 3, 4, 7, 6, 12, 8, 7, 13, 18, 12, 28, 14, 24, 24, 7, 18, 39, 20, 42, 32, 36, 24, 28, 31, 42, 40, 56, 30, 72, 32, 7, 48, 54, 48, 91, 38, 60, 56, 42, 42, 96, 44, 84, 78, 72, 48, 28, 57, 93, 72, 98, 54, 120, 72, 56, 80, 90, 60, 168, 62, 96, 104, 7, 84, 144, 68

Offset

1,2

Comments

First differs from A284341 at n = 81 = 3^4: a(81) = 40, while A284341(81) = 121.

The number of these divisors is A377519(n), and the largest of them is A377518(n).

Links

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

Formula

a(n) = A000203(A377518(n)).

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

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

Sum_{k=1..n} a(k) ~ c * n^2 / 2, where c = zeta(2) * Product_{p prime} (1 - 1/p^(p+1)) = 1.42145673335960701365... .

Mathematica

f[p_, e_] := (p^(Min[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(f[i, 1], f[i, 2]) + 1) - 1)/(f[i, 1] - 1)); }

Crossrefs

Cf. A000203, A013661, A207481, A284341, A377517, A377518, A377519.

Sequence in context: A366744 A073185 A284341 * A073183 A353900 A366903

Adjacent sequences: A377517 A377518 A377519 * A377521 A377522 A377523

Keyword

nonn,easy,mult

Author

Amiram Eldar, Oct 30 2024

Status

approved