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%I #10 Jun 17 2018 02:05:35
%S 2,3,5,6,7,10,11,12,13,14,15,17,18,19,20,21,23,26,29,30,31,33,34,35,
%T 37,38,40,41,43,44,45,46,47,48,51,53,54,55,56,57,58,59,61,63,65,67,68,
%U 71,72,73,74,75,78,79,80,83,85,86,88,89,90,93,96,97,98,101,103,105,107
%N Numbers k such that usigma(k) - 1 is a prime (cf. A034448).
%H Harry J. Smith, <a href="/A065872/b065872.txt">Table of n, a(n) for n = 1..1000</a>
%t f[n_] := Block[ {a = FactorInteger[n], k = l = s = 1}, l = Length[a]; While[k <= l, s = s * (a[[k, 1]]^a[[k, 2]] + 1); k++ ]; Return[s]]; Select[ Range[200], PrimeQ[ f[ # ] - 1] & ]
%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 (isprime(usigma(m) - 1), write("b065872.txt", n++, " ", m); if (n==1000, return)) ) } \\ _Harry J. Smith_, Nov 02 2009
%Y Cf. A034448.
%K nonn
%O 1,1
%A _Robert G. Wilson v_, Dec 07 2001