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A296375 Least x such that sigma(x) = prime(n)+1, where sigma = A000203.

%I A296375 #31 Dec 28 2017 00:57:17
%S A296375 2,3,5,7,6,13,10,19,14,29,21,37,20,43,33,34,24,61,67,30,73,57,44,40,
%T A296375 52,101,63,85,109,74,93,86,137,76,149,111,157,163,60,173,88,117,105,
%U A296375 193,197,199,211,84,147,229,90,114,241,96,257,215,136,201,277,281,283,164,172,126,313,317,331,337
%N A296375 Least x such that sigma(x) = prime(n)+1, where sigma = A000203.
%C A296375 a(n) <= prime(n).
%H A296375 Charles R Greathouse IV, <a href="/A296375/b296375.txt">Table of n, a(n) for n = 1..10000</a>
%e A296375 For n=5, prime(5)+1 = 12; sigma(x) = 12 for x=6 and x=11, so a(5) = 6.
%p A296375 N:= 100: # to get a(1)..a(N)
%p A296375 for i from 1 to N do T(ithprime(i)):= i od:
%p A296375 count:= 0:
%p A296375 for n from 1 while count < N do
%p A296375 v:= numtheory:-sigma(n);
%p A296375 if T(v)::posint then
%p A296375   A[T(v)]:= n;
%p A296375   T(v):= 0;
%p A296375     count:= count+1;
%p A296375   fi
%p A296375 od:
%p A296375 seq(A[i],i=1..N);
%o A296375 (PARI) first(n) = my(res = vector(n), p = 2); for(k=1, n, for(x=2, p, if(sigma(x) == p+1, res[k] = x; break())); p = nextprime(p+1)); res \\ _Iain Fox_, Dec 28 2017
%o A296375 (PARI) first(n)=my(v=vector(n),P=primes(n),left=n,t); forfactored(x=2,P[n], t=setsearch(P,sigma(x)-1); if(t && v[t]==0, v[t]=x[1]; if(left--==0, return(v)))) \\ _Charles R Greathouse IV_, Dec 28 2017
%Y A296375 Cf. A066077.
%K A296375 nonn
%O A296375 1,1
%A A296375 _Robert Israel_, Dec 27 2017