OFFSET
1,6
LINKS
Antti Karttunen, Table of n, a(n) for n = 1..65537
FORMULA
a(1) = 1, a(p) = 1, a(pq) = pq+1, a(pq...z) = [(p+1)*(q+1)*…*(z+1)] - (p+q+...+z), a(p^k) = 1, for p, q = primes, k = natural numbers, pq...z = product of k (k > 2) distinct primes p, q, ..., z.
a(n) = Sum_{d|n} d * (1 - [omega(n) = 1]), where omega is the number of distinct prime factors (A001221) and [ ] is the Iverson bracket. - Wesley Ivan Hurt, Jan 28 2021
EXAMPLE
For n = 12, set of such divisors is {1, 6, 12}; a(12) = 1+6+12 = 19.
MATHEMATICA
Array[Plus @@ (Select[Divisors[#], (Length[FactorInteger[#]] > 1) &]) &, 100] + 1 (* Robert P. P. McKone, Jan 28 2021 *)
PROG
(PARI) A178637(n) = sumdiv(n, d, (omega(d)!=1)*(d)); \\ Antti Karttunen, Aug 06 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Jaroslav Krizek, Dec 25 2010
STATUS
approved