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

1,4

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

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).

Mathematica

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

Prog

(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))); }

Crossrefs

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

Sequence in context: A204007 A242404 A145295 * A360722 A091051 A183097

Adjacent sequences: A366987 A366988 A366989 * A366991 A366992 A366993

Keyword

nonn,easy,mult

Author

Amiram Eldar, Oct 31 2023

Status

approved