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 A064193 Numbers whose product of divisors and sum of unitary divisors are both squares. 1

%I

%S 1,8,22,24,66,70,94,115,119,170,210,214,217,228,265,282,310,322,345,

%T 357,382,385,490,497,510,517,522,527,580,642,651,679,710,742,745,782,

%U 795,862,889,920,930,935,948,952,966,970,1066,1146,1155,1174,1177,1197

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

%H Harry J. Smith, <a href="/A064193/b064193.txt">Table of n, a(n) for n = 1..1000</a>

%o (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,",")))

%o (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

%Y Cf. A034448, A007955.

%K easy,nonn

%O 1,2

%A _Jason Earls_, Oct 14 2001

%E Erroneous PARI program of Sep 09 2009 deleted by _Harry J. Smith_, Sep 23 2009

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Last modified March 23 16:52 EDT 2019. Contains 321432 sequences. (Running on oeis4.)