|
|
A348219
|
|
a(n) = tau(n) - omega(n) + n * Sum_{p|n} 1/p.
|
|
1
|
|
|
1, 2, 2, 4, 2, 7, 2, 7, 5, 9, 2, 14, 2, 11, 10, 12, 2, 19, 2, 18, 12, 15, 2, 26, 7, 17, 12, 22, 2, 36, 2, 21, 16, 21, 14, 37, 2, 23, 18, 34, 2, 46, 2, 30, 28, 27, 2, 48, 9, 39, 22, 34, 2, 51, 18, 42, 24, 33, 2, 71, 2, 35, 34, 38, 20, 66, 2, 42, 28, 64, 2, 70, 2, 41, 44, 46
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
COMMENTS
|
For each divisor d of n, add n/d if d is prime, otherwise add 1. For example, a(9) = 5 can be found using its divisors 1,3,9 to get 1 + 9/3 + 1 = 5.
If p is prime, then a(p) = 2 since we have a(p) = tau(p) - omega(p) + p/p = 2 - 1 + 1 = 2.
|
|
LINKS
|
|
|
FORMULA
|
a(n) = Sum_{d|n} (n/d)^c(d), where c is the prime characteristic (A010051).
a(prime(n)) = 2.
|
|
PROG
|
(PARI)
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|