A064710 - OEIS

%I #31 Jan 07 2020 09:07:12

%S 1,22,66,70,81,94,115,119,170,210,214,217,265,282,310,322,343,345,357,

%T 364,382,385,472,497,510,517,527,642,651,679,710,742,745,782,795,820,

%U 862,884,889,930,935,966,970,1029,1066,1080,1092,1146,1155,1174

%N Numbers k such that the sum of divisors of k and the product of divisors of k are both perfect squares.

%H Amiram Eldar, <a href="/A064710/b064710.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1000 from Harry J. Smith)

%t psQ[n_]:=Module[{d=Divisors[n]},IntegerQ[Sqrt[Total[d]]] && IntegerQ[ Sqrt[Times@@d]]]; Select[Range[1200],psQ] (* _Harvey P. Dale_, Mar 07 2012 *)

%o (PARI) pd(n) = n^(numdiv(n)/2);

%o for(n=1,2000, if(issquare(sigma(n)) && issquare(pd(n)), print1(n,", ")))

%o (PARI) pd(n)= { d=numdiv(n); if (d%2, round(sqrt(n))^d, n^(d/2)) }

%o { n=0; for (m=1, 10^9, if (issquare(sigma(m)) && issquare(pd(m)), write("b064710.txt", n++, " ", m); if (n==1000, break)) ) } \\ _Harry J. Smith_, Sep 23 2009

%o (Sage) [n for n in (1..100000) if sigma(n).is_square()and prod(divisors(n)).is_square()] # _Giuseppe Coppoletta_, Dec 16 2014

%Y Cf. A007955, A000203.

%K easy,nonn

%O 1,2

%A _Jason Earls_, Oct 13 2001

%E Corrected by _Harvey P. Dale_, Oct 23 2001