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A064710
Numbers k such that the sum of divisors of k and the product of divisors of k are both perfect squares.
3
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
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
Sequence in context: A124715 A126376 A136604 * A246415 A164136 A041946
KEYWORD
easy,nonn
AUTHOR
Jason Earls, Oct 13 2001
EXTENSIONS
Corrected by Harvey P. Dale, Oct 23 2001
STATUS
approved

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Last modified September 20 07:49 EDT 2024. Contains 376067 sequences. (Running on oeis4.)