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
Links
- Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Harry J. Smith)
Programs
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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 *) -
PARI
pd(n) = n^(numdiv(n)/2); for(n=1,2000, if(issquare(sigma(n)) && issquare(pd(n)), print1(n,", ")))
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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
Extensions
Corrected by Harvey P. Dale, Oct 23 2001