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%I #20 Apr 13 2024 15:02:16
%S 3,5,6,13,18,20,27,37,50,61,73,96,157,193,242,277,313,397,421,457,486,
%T 541,613,661,673,722,733,757,877,997,1093,1153,1201,1213,1237,1321,
%U 1381,1453,1621,1657,1682,1753,1873,1933,1993,2017,2137,2341,2473,2557
%N Numbers k such that usigma(k) / tau(k) is prime.
%H Harry J. Smith, <a href="/A064519/b064519.txt">Table of n, a(n) for n = 1..1000</a>
%o (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); }
%o for(n=1,5000, if(usigma(n)%numdiv(n)==0 && isprime(usigma(n)/numdiv(n)), print1(n,", ")))
%o (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 ((u=usigma(m))%(d=numdiv(m))==0 && isprime(u/d), write("b064519.txt", n++, " ", m); if (n==1000, break)) ) } \\ _Harry J. Smith_, Sep 17 2009
%Y Cf. A034448, A000005.
%K easy,nonn,changed
%O 1,1
%A _Jason Earls_, Oct 07 2001
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