

A135581


The 5th divisor of numbers with 25 divisors.


5



6, 8, 8, 15, 21, 11, 13, 27, 16, 35, 16, 27, 16, 27, 55, 27, 16, 16, 16, 65, 27, 16, 77, 16, 85, 16, 29, 91, 31, 16, 95, 16, 37, 115, 16, 119, 16, 41, 43, 133, 16, 47, 16, 143, 125, 16, 125, 16, 53, 161, 16, 59, 16, 61, 125, 187, 16, 67, 16, 203, 125, 16, 209, 71, 16, 125
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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 LaprÃ©, 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

Cf. A005179, A137488, A200722, A201266.
Sequence in context: A315947 A315948 A315949 * A182601 A261506 A021596
Adjacent sequences: A135578 A135579 A135580 * A135582 A135583 A135584


KEYWORD

nonn,look,easy,changed


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



