A064193 Numbers whose product of divisors and sum of unitary divisors are both squares.

1, 8, 22, 24, 66, 70, 94, 115, 119, 170, 210, 214, 217, 228, 265, 282, 310, 322, 345, 357, 382, 385, 490, 497, 510, 517, 522, 527, 580, 642, 651, 679, 710, 742, 745, 782, 795, 862, 889, 920, 930, 935, 948, 952, 966, 970, 1066, 1146, 1155, 1174, 1177, 1197

Offset

1,2

Links

Harry J. Smith, Table of n, a(n) for n = 1..1000

Prog

(PARI) a(n) = n^(numdiv(n)/2); {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, 3000, if(issquare(a(n)) && issquare(usigma(n)), print1(n, ", ")))
(PARI) pd(n)= { d=numdiv(n); if (d%2, round(sqrt(n))^d, n^(d/2)) } 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(pd(m)) && issquare(usigma(m)), write("b064193.txt", n++, " ", m); if (n==1000, break)) ) } \\ Harry J. Smith, Sep 23 2009

Crossrefs

Cf. A034448, A007955.

Sequence in context: A215600 A304301 A236917 * A301482 A213017 A305515

Adjacent sequences: A064190 A064191 A064192 * A064194 A064195 A064196

Keyword

easy,nonn

Author

Jason Earls, Oct 14 2001

Extensions

Erroneous PARI program of Sep 09 2009 deleted by Harry J. Smith, Sep 23 2009

Status

approved