A064498 Numbers k such that the sum of unitary divisors of k^2 is a square.

1, 42, 120, 156, 246, 287, 1434, 1673, 2016, 5256, 9799, 11808, 18330, 19740, 21385, 34440, 39990, 44772, 45990, 46655, 57270, 60156, 66815, 68832, 102648, 115620, 125255, 149472, 156570, 170820, 182665, 195510, 200760, 208182, 223944, 224196

Offset

1,2

Links

Amiram Eldar, Table of n, a(n) for n = 1..1000 (terms 1..100 from Harry J. Smith)

Mathematica

sudsQ[n_]:=Module[{uds=Sort[Flatten[Outer[Times, Sequence@@({1, #}&/@ Power@@@FactorInteger[n^2])]]]}, IntegerQ[Sqrt[Total[uds]]]]; Join[{1}, Select[Range[230000], sudsQ]] (* Harvey P. Dale, Dec 09 2011 *)

Prog

(PARI) {usigma(n, s=1, fac, i)= fac=factor(n); for(i=1, matsize(fac)[1], s=s*(1+fac[i, 1]^fac[i, 2]); ); return(s); }
for(n=1, 10^6, if(issquare(usigma(n^2)), print1(n, " ")))
(PARI) usigma(n)= { local(f, s=1); f=factor(n); for(i=1, matsize(f)[1], s*=1 + f[i, 1]^f[i, 2]); return(s) }
{ n=0; for (m=1, 10^9, if (issquare(usigma(m^2)), write("b064498.txt", n++, " ", m); if (n==100, break)) ) } \\ Harry J. Smith, Sep 16 2009

Crossrefs

Cf. A034448 (usigma), A008847 (similar, with sigma).

Sequence in context: A335064 A128674 A239590 * A113518 A044293 A044674

Adjacent sequences: A064495 A064496 A064497 * A064499 A064500 A064501

Keyword

nonn

Author

Jason Earls, Oct 05 2001

Status

approved