A064710 Numbers k such that the sum of divisors of k and the product of divisors of k are both perfect squares.

1, 22, 66, 70, 81, 94, 115, 119, 170, 210, 214, 217, 265, 282, 310, 322, 343, 345, 357, 364, 382, 385, 472, 497, 510, 517, 527, 642, 651, 679, 710, 742, 745, 782, 795, 820, 862, 884, 889, 930, 935, 966, 970, 1029, 1066, 1080, 1092, 1146, 1155, 1174

Offset

1,2

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Harry J. Smith)

Mathematica

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

Prog

(PARI) pd(n) = n^(numdiv(n)/2);
for(n=1, 2000, if(issquare(sigma(n)) && issquare(pd(n)), print1(n, ", ")))
(PARI) pd(n)= { d=numdiv(n); if (d%2, round(sqrt(n))^d, n^(d/2)) }
{ 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
(Sage) [n for n in (1..100000) if sigma(n).is_square()and prod(divisors(n)).is_square()] # Giuseppe Coppoletta, Dec 16 2014

Crossrefs

Cf. A007955, A000203.

Sequence in context: A124715 A126376 A136604 * A246415 A164136 A041946

Adjacent sequences: A064707 A064708 A064709 * A064711 A064712 A064713

Keyword

easy,nonn

Author

Jason Earls, Oct 13 2001

Extensions

Corrected by Harvey P. Dale, Oct 23 2001

Status

approved