A366990 The sum of divisors of n that are terms of A056166.

1, 1, 1, 5, 1, 1, 1, 13, 10, 1, 1, 5, 1, 1, 1, 13, 1, 10, 1, 5, 1, 1, 1, 13, 26, 1, 37, 5, 1, 1, 1, 45, 1, 1, 1, 50, 1, 1, 1, 13, 1, 1, 1, 5, 10, 1, 1, 13, 50, 26, 1, 5, 1, 37, 1, 13, 1, 1, 1, 5, 1, 1, 10, 45, 1, 1, 1, 5, 1, 1, 1, 130, 1, 1, 26, 5, 1, 1, 1, 13

Offset: 1

Author

Amiram Eldar, Oct 31 2023

Keywords

• nonn
• easy
• mult

Comments

The number of these divisors is A095691(n) and the largest of them is A366993(n).

Links

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

Crossrefs

Cf. A005117, A056166, A095691, A366988, A366993.

Programs

Mathematica

f[p_, e_] := 1 + Total[p^Select[Range[e], PrimeQ]]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100]

PARI

a(n) = {my(f = factor(n)); prod(i = 1, #f~, 1 + sum(j = 1, f[i, 2], if(isprime(j), f[i, 1]^j)));}

Formula

Multiplicative with a(p^e) = 1 + Sum_{primes q <= e} p^q.

a(n) >= 1, with equality if and only if n is squarefree (A005117).