OFFSET
1,2
COMMENTS
The values of n are 1, 313, 3^3*151, 7*37*163, 2^3*19*499, 3^3*151*313, 2^3*19*37*439, 37*439*499, ...
Corresponding n^2 values are 1, 97969, 16621929, 1782275089, ...
The next two primes in the sequence (after 313 and 2288805793) are 86136917171761 and 23666840016182721134955337. - Giovanni Resta, Apr 26 2017
EXAMPLE
313 is a term because the divisors of 313^2 are 1, 313 and 313^2. Average of 1, 313 and 313^2 is 32761 that is 181^2.
MATHEMATICA
Select[Range[10^5], IntegerQ@ Sqrt@ Mean@ Divisors[#^2] &] (* Michael De Vlieger, Apr 29 2016 *)
PROG
(PARI) lista(nn) = for(n=1, nn, if(sigma(n^2) % numdiv(n^2) == 0 && issquare(sigma(n^2)/numdiv(n^2)), print1(n, ", ")));
(PARI) is(n)=my(f=factor(n), s, d); f[, 2]*=2; s=sigma(f); d=numdiv(f); s%d==0 && issquare(s/d) \\ Charles R Greathouse IV, Apr 29 2016
CROSSREFS
KEYWORD
nonn
AUTHOR
Altug Alkan, Apr 29 2016
EXTENSIONS
a(10)-a(16) from Charles R Greathouse IV, Apr 29 2016
a(17)-a(24) from Giovanni Resta, Apr 26 2017
STATUS
approved