OFFSET
2,2
COMMENTS
Also the number of factors of 2*n^2 which are less than n. - Vladeta Jovovic, Dec 12 2002
Also the number of factors of 2*n^2 which are greater than 2*n, so a(n) = tau(2*n^2)-1-A055081(n). - Vladeta Jovovic, Dec 13 2002
FORMULA
No general formula is known but let k be a positive integer, p and q distinct odd primes then a(2^k)=k a(p^k)=2*k a(p*q)= 7 or 8 if p >13 a(2*p)= 5 if p>5 a(9*p^2)= 23 .... Asymptotic formula: (1/n)*sum(i=1, n, a(i))= log(n)*log(log(n))+o(log(n)).
EXAMPLE
a(2)=1 because (2^2+1)/(2-1) is the only integer of this form.
CROSSREFS
KEYWORD
nonn
AUTHOR
Benoit Cloitre, Jan 17 2002
EXTENSIONS
Corrected by Vladeta Jovovic, Dec 12 2002
STATUS
approved