OFFSET
1,1
COMMENTS
n=1 means the first number that has 25 divisors (1296), 6 is the 5th divisor of 1296. The second number with 25 divisors is 10000 and its 5th divisor is 8
This is one example of such a sequence where the divisor index is the square root of the total number of divisors (self included).
Other examples would be the 6th divisor of numbers with 36 divisors, 7th divisor of numbers with 49 divisors, etc.
Choice of the square root is arbitrary.
All but 16 primes {2, 3, 5, 7, 17, 19, 23, 83, 89, 97, 101, 103, 107, 109, 113} are in this sequence; p^3 and p^4 are in this sequence for all prime p; pq is in this sequence for all prime p and q with p < q < p^2. No other terms are members. - Charles R Greathouse IV, Nov 28 2011
LINKS
Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
Laurens Lapré, Natural division.
Wikipedia, Divisor function
EXAMPLE
a(1) = 6 because 6 is the 5th divisor of 1296 and 1296 is the first number with 25 divisors.
a(2) = 8 because 8 is the 5th divisor of 10000 and 10000 is the second number with 25 divisors.
MATHEMATICA
upto=10^10; With[{max1=Ceiling[Power[upto, (4)^-1]], max2=Ceiling[ Power[ upto, (24)^-1]]}, Take[Divisors[#][[5]]&/@Select[Union[Join[ Range[ max2]^24, Times@@@(Subsets[Range[max1], {2}]^4)]], DivisorSigma[0, #] == 25&], Ceiling[max1/4]]] (* Harvey P. Dale, Nov 25 2011 *)
PROG
(Haskell)
a135581 n = [d | d <- [1..], a137488 n `mod` d == 0] !! 4
-- Reinhard Zumkeller, Nov 29 2011
CROSSREFS
KEYWORD
AUTHOR
G. H. Ens (GerardEns(AT)gmail.com), Feb 24 2008
EXTENSIONS
Corrected and extended by R. J. Mathar, Apr 21 2008. The original entries were wrong from the 16th term onwards.
STATUS
approved