OFFSET
1,1
COMMENTS
For every n>1 sigma(n)^2 > sigma(n^2).
Lim_{n->inf} a(n)/n appears to exist and is near 8.0; e.g., a(124094) = 1000000. - Paul D. Hanna, Sep 22 2011
We also have a(12438441) = 10^8, a(124240921) = 10^9, and a(1242729194) = 10^10. - Giovanni Resta, Jun 15 2018
LINKS
Paul D. Hanna, Table of n, a(n) for n = 1..1000
EXAMPLE
The limit a(n)/n seems to be near 8.0:
n a(n) a(n)/n
------- -------- ----------
124094 1000000 8.05840...
248310 2000000 8.05444...
372503 3000000 8.05362...
496826 4000000 8.05110...
621163 5000000 8.04941...
745602 6000000 8.04718...
870189 7000000 8.04422...
994799 8000000 8.04182...
1119336 9000000 8.04048...
1243884 10000000 8.03933...
MATHEMATICA
Select[Range[500], DivisorSigma[1, #]^2>2DivisorSigma[1, #^2]&] (* Harvey P. Dale, Mar 30 2011 *)
PROG
(PARI) {for(n=1, 8000, if(2*sigma(n^2)-sigma(n)^2 < 0, print1(n, ", ")))} \\ Paul D. Hanna, Sep 22 2011
CROSSREFS
KEYWORD
nonn
AUTHOR
Benoit Cloitre, Feb 07 2002
STATUS
approved