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A071390 Least number m such that sigma(m) - phi(m) = n, or 0 if no such m exists.

%I A071390 #17 Apr 02 2020 11:42:35
%S A071390 0,2,0,0,4,0,9,0,0,6,8,0,0,10,49,15,0,14,0,21,0,27,16,12,0,22,169,33,
%T A071390 0,26,0,39,18,20,289,65,0,34,361,51,0,38,0,28,0,0,32,95,0,46,0,24,0,
%U A071390 45,0,115,0,0,841,161,0,58,961,30,0,62,81,63,0,0,0,155,50,40,1369,217,0,74
%N A071390 Least number m such that sigma(m) - phi(m) = n, or 0 if no such m exists.
%C A071390 For n <> 2, a(n) < n^2/4. - _Robert Israel_, Apr 02 2020
%H A071390 Robert Israel, <a href="/A071390/b071390.txt">Table of n, a(n) for n = 1..2000</a>
%F A071390 a(n) = Min{x; A000203(x)-A000010(x)=n} or a(n)=0 if no solution exists.
%e A071390 n=255: a(255) = 16129 = 127^2, sigma(16129) = 16257, phi(16129) = 16002, 16257 - 16002 = 255 = n. Squares of primes are often solutions (4, 9, 49, 169, 289, 361, etc.).
%p A071390 N:= 100: # for a(1)..a(N)
%p A071390 V:= Vector(N):
%p A071390 for m from 2 to N^2/4 do
%p A071390   v:= numtheory:-sigma(m)-numtheory:-phi(m);
%p A071390   if v <= N and V[v]=0 then V[v]:= m fi
%p A071390 od:
%p A071390 convert(V,list); # _Robert Israel_, Apr 02 2020
%t A071390 f[x_] := DivisorSigma[1, x]-EulerPhi[x] t=Table[0, {100}]; Do[c=f[n]; If[c<101&&t[[c]]==0, t[[c]]=n], {n, 1, 1000}]; t
%Y A071390 Cf. A000010, A000203, A065387, A051612, A071391.
%K A071390 nonn
%O A071390 1,2
%A A071390 _Labos Elemer_, May 23 2002