cp's OEIS Frontend

A272442 Numbers n such that the average of the positive divisors of n^2 is a square.

%I A272442 #24 Apr 26 2017 10:24:32
%S A272442 1,313,4077,42217,75848,1276101,2468936,8105257,13213921,23740424,
%T A272442 76136648,172118709,249948601,296474857,309232296,772776968,
%U A272442 1236329761,1254551521,2288805793,2372141576,2410951561,2536945441,3202075016,10065852072
%N A272442 Numbers n such that the average of the positive divisors of n^2 is a square.
%C A272442 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, ...
%C A272442 Corresponding n^2 values are 1, 97969, 16621929, 1782275089, ...
%C A272442 The next two primes in the sequence (after 313 and 2288805793) are 86136917171761 and 23666840016182721134955337. - _Giovanni Resta_, Apr 26 2017
%e A272442 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.
%t A272442 Select[Range[10^5], IntegerQ@ Sqrt@ Mean@ Divisors[#^2] &] (* _Michael De Vlieger_, Apr 29 2016 *)
%o A272442 (PARI) lista(nn) = for(n=1, nn, if(sigma(n^2) % numdiv(n^2) == 0 && issquare(sigma(n^2)/numdiv(n^2)), print1(n, ", ")));
%o A272442 (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
%Y A272442 Cf. A000290, A003601, A144695.
%K A272442 nonn
%O A272442 1,2
%A A272442 _Altug Alkan_, Apr 29 2016
%E A272442 a(10)-a(16) from _Charles R Greathouse IV_, Apr 29 2016
%E A272442 a(17)-a(24) from _Giovanni Resta_, Apr 26 2017