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A064519
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Numbers k such that usigma(k) / tau(k) is prime.
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1
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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
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OFFSET
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1,1
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LINKS
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PROG
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(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
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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