A228015 - OEIS

%I #16 Aug 22 2014 12:55:04

%S 4,7,22,11,16,29,26,31,56,16,17,27,56,24,21,49,62,24,33,71,35,32,35,

%T 51,94,48,49,42,43,56,86,46,53,121,49,62,176,52,59,95,106,80,65,72,

%U 332,68,214,111,73,74,97,74,99,111,232,181,470,88,89,275,91,2019,132,98,89,128,212,114,156,257

%N Smallest integer m > n such that phi(m+n) = sigma(m-n).

%C It seems that for all n, a(n)/n <= 2019/62. [_Farideh Firoozbakht_, Aug 22 2014]

%H Alois P. Heinz, <a href="/A228015/b228015.txt">Table of n, a(n) for n = 1..10000</a>

%e For n=1 and m = 2 and 3 phi(m+1) != sigma(m-1), but for m=4 phi(m+1) = sigma(m-1). Thus a(1) = 4.

%p with(numtheory):

%p a:= proc(n) local m;

%p       for m from n+1 while phi(m+n)<>sigma(m-n) do od; m

%p     end:

%p seq(a(n), n=1..80);  # _Alois P. Heinz_, Aug 05 2013

%t a[m_]:=(For[n=m+1,DivisorSigma[1,n-m]!=EulerPhi[n+m],n++];n);Table[a[n],{n,70}]

%K nonn

%O 1,1

%A _Farideh Firoozbakht_, Aug 02 2013