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 A064519 Numbers n such that usigma(n) / tau(n) is prime. 1
 3, 5, 6, 13, 18, 20, 27, 37, 50, 61, 73, 96, 157, 193, 242, 277, 313, 397, 421, 457, 486, 541, 613, 661, 673, 722, 733, 757, 877, 997, 1093, 1153, 1201, 1213, 1237, 1321, 1381, 1453, 1621, 1657, 1682, 1753, 1873, 1933, 1993, 2017, 2137, 2341, 2473, 2557 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS Harry J. Smith, Table of n, a(n) for n = 1..1000 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, 5000, if(usigma(n)%numdiv(n)==0 && isprime(usigma(n)/numdiv(n)), 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 ((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 CROSSREFS Cf. A034448, A000005. Sequence in context: A139013 A108337 A285534 * A048968 A185737 A092862 Adjacent sequences:  A064516 A064517 A064518 * A064520 A064521 A064522 KEYWORD easy,nonn AUTHOR Jason Earls, Oct 07 2001 STATUS approved

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Last modified October 17 12:21 EDT 2019. Contains 328111 sequences. (Running on oeis4.)