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

Author

Amiram Eldar, Sep 14 2023

Keywords

• nonn
• easy
• mult

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

Crossrefs

Cf. A072873, A327939, A332653, A365632.

Programs

Mathematica

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

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));}

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... .