OFFSET
1,2
COMMENTS
The numbers of terms not exceeding 10^k, for k = 1, 2, ..., are 3, 35, 326, 3275, 33090, 332435, 3327555, 33283964, 332868092, 3328794682, ... . Apparently, the asymptotic density of this sequence exists and equals 0.3328... . - Amiram Eldar, Nov 28 2023
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Harry J. Smith)
FORMULA
EXAMPLE
n=2: a(2) = 6 because the number of divisors of 6^2 is 9, a square.
MATHEMATICA
Select[Range[200], IntegerQ[Sqrt[DivisorSigma[0, #^2]]]&] (* Harvey P. Dale, Jun 06 2012 *)
PROG
(PARI) j=[]; for(n=1, 500, a=numdiv(n^2); if(issquare(a), j=concat(j, n))); j
(PARI) n=0; for (m=1, 10^9, if(issquare(numdiv(m^2)), write("b063774.txt", n++, " ", m); if (n==1000, break))) \\ Harry J. Smith, Aug 30 2009
(PARI) is(n)=my(f=factor(n)[, 2]); issquare(prod(i=1, #f, 2*f[i]+1)) \\ Charles R Greathouse IV, Sep 18 2015
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Jason Earls, Aug 15 2001
STATUS
approved