A064443 Numbers k such that usigma(k) is a square and sets a new record for such squares.

1, 3, 8, 22, 66, 170, 210, 490, 510, 930, 1470, 2130, 2910, 3810, 5406, 5970, 7230, 7590, 10110, 12306, 13470, 14322, 17310, 17490, 23142, 26430, 29010, 32430, 37470, 42546, 44814, 49170, 58674, 69330, 73830, 86610, 87780, 96690

Offset

1,2

Links

Amiram Eldar, Table of n, a(n) for n = 1..250 (terms 1..100 from Harry J. Smith)

Mathematica

usigma[1] = 1; usigma[n_] := Times @@ (1 + Power @@@ FactorInteger@n);  um = 0; s = {}; Do[u = usigma[n]; If[IntegerQ@Sqrt[u] && u > um, um = u; AppendTo[s, n]], {n, 1, 10^5}]; s (* Amiram Eldar, Jul 29 2019 *)

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); a=0; j=[]; for(n=1, 10^5, x=usigma(n); if(issquare(x), b=x; if(b>a, a=b; j=concat(j, n)))); j
(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=a=0; for (m=1, 10^9, if (issquare(b=usigma(m)), if(b>a, a=b; write("b064443.txt", n++, " ", m); if (n==100, break))) ) } \\ Harry J. Smith, Sep 14 2009

Crossrefs

Cf. A034448.

Sequence in context: A290898 A117420 A003101 * A000732 A092090 A011958

Adjacent sequences: A064440 A064441 A064442 * A064444 A064445 A064446

Keyword

nonn

Author

Jason Earls, Oct 01 2001

Status

approved