A365633 The sum of divisors of n that are terms of A072873.

1, 1, 1, 3, 1, 1, 1, 3, 1, 1, 1, 3, 1, 1, 1, 7, 1, 1, 1, 3, 1, 1, 1, 3, 1, 1, 4, 3, 1, 1, 1, 7, 1, 1, 1, 3, 1, 1, 1, 3, 1, 1, 1, 3, 1, 1, 1, 7, 1, 1, 1, 3, 1, 4, 1, 3, 1, 1, 1, 3, 1, 1, 1, 15, 1, 1, 1, 3, 1, 1, 1, 3, 1, 1, 1, 3, 1, 1, 1, 7, 4, 1, 1, 3, 1, 1, 1

Offset

1,4

Comments

The number of these divisors is A365632(n) and the largest of them is A327939(n).

Links

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

Formula

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

Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = Product_{p prime} (A332653(p)/(p^(p-1)-1) - 1/(p*(p-1))) = 2.253624924813... .

Mathematica

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

Crossrefs

Cf. A072873, A327939, A332653, A365632.

Sequence in context: A093148 A069292 A368336 * A091842 A306346 A060901

Adjacent sequences: A365630 A365631 A365632 * A365634 A365635 A365636

Keyword

nonn,easy,mult

Author

Amiram Eldar, Sep 14 2023

Status

approved