login
A366990
The sum of divisors of n that are terms of A056166.
3
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
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
KEYWORD
nonn,easy,mult
AUTHOR
Amiram Eldar, Oct 31 2023
STATUS
approved