OFFSET
1,2
COMMENTS
From Jianing Song, Aug 30 2021: (Start)
a(n) is the smallest number whose square has exactly 2n-1 divisors.
a(n) is the earliest occurrence of 2n-1 in A048691. (End)
LINKS
David W. Wilson, Table of n, a(n) for n = 1..1000 (terms 122, 365 and 608 corrected by Amiram Eldar, Nov 08 2024)
FORMULA
a(n+1) <= 2^n.
From Labos Elemer, May 22 2001: (Start)
a(n) = sqrt(A061283(n)).
a(n) = sqrt(Min{k| A000005(k)=2n-1}).
a((p+1)/2) = 2^((p-1)/2) = 2^A005097(i) if p is the i-th odd prime. [Corrected by Jianing Song, Aug 30 2021] (End)
a(n) is the least k such that (tau(k^2) + 1)/2 = n. - Vladeta Jovovic, Aug 01 2001
EXAMPLE
a(1)=1 and a(2)=2 because 1/2 = 1/3 + 1/6 = 1/4 + 1/4.
a(3)=4 because 1/4 = 1/5 + 1/20 = 1/6 + 1/12 = 1/8 + 1/8.
a(4)=8 because 1/8 = 1/9 + 1/72 = 1/10 + 1/40 = 1/12 + 1/24 = 1/16 + 1/16.
a(5)=6 because 1/6 = 1/7 + 1/42 = 1/8 + 1/24 = 1/9 + 1/18 = 1/10 + 1/15 = 1/12 + 1/12.
MATHEMATICA
f[j_, n_] := (Times @@ (j(Last /@ FactorInteger[n]) + 1) + j - 1)/j; t = Table[0, {50}]; Do[a = f[2, n]; If[a < 51 && t[[a]] == 0, t[[a]] = n; Print[{a, n}]], {n, 2^30}] (* Robert G. Wilson v, Aug 03 2005 *)
PROG
(PARI) a(n) = {k = 1; while (numdiv(k^2) != (2*n-1), k++); return (k); }; \\ Amiram Eldar, Jan 07 2019 after Michel Marcus at A071571
CROSSREFS
KEYWORD
nonn
AUTHOR
EXTENSIONS
Entry revised by N. J. A. Sloane, Aug 14 2005
Offset corrected by David W. Wilson, Dec 27 2018
STATUS
approved