OFFSET
1,2
LINKS
Antti Karttunen, Table of n, a(n) for n = 1..20000
FORMULA
For n > 1, a(n) = n + n * Sum_(p|n) 1 / p, where p are primes dividing n.
a(n) = A069359(n) + n.
a(n) = A080339(n) * A000027(n), where operation * denotes Dirichlet convolution, i.e. convolution of type: a(n) = Sum_{d|n} b(d) * c(n/d).
For p, q = distinct primes, a(p) = p + 1, a(pq) = pq - 1.
From Antti Karttunen, Nov 12 2021: (Start)
(End)
For p prime, k>=1, a(p^k) = p^(k-1) * (p+1). - Bernard Schott, Nov 12 2021
EXAMPLE
For n = 6: a(6) = 6 * (1/1 + 1/2 + 1/3) = 11.
MATHEMATICA
a[n_] := n * DivisorSum[n, 1/# &, !CompositeQ[#] &]; Array[a, 100] (* Amiram Eldar, Nov 12 2021 *)
PROG
(PARI) A230593(n) = sumdiv(n, d, ((1==d)||isprime(d))*(n/d)); \\ Antti Karttunen, Nov 12 2021
CROSSREFS
KEYWORD
nonn
AUTHOR
Jaroslav Krizek, Oct 25 2013
STATUS
approved