cp's OEIS Frontend

A244448 a(n) is the smallest integer m such that m-n is composite and phi(m-n) + sigma(m+n) = phi(m+n) + sigma(m-n).

%I A244448 #27 Apr 10 2020 14:31:12
%S A244448 4,153,442,213,179,120,46,37,47,264,145416,1101,107,79,71,78,716,637,
%T A244448 98,249,71,126,13258,1243,119,163,119,131,140497,381,191,156,101,169,
%U A244448 1574,315,151,193,167,2158,148,104,202,289,1969,882,2572,428,251,357,314,283
%N A244448 a(n) is the smallest integer m such that m-n is composite and phi(m-n) + sigma(m+n) = phi(m+n) + sigma(m-n).
%C A244448 For each n, a(n) > n and like a(n)-n, a(n)+n is also composite.
%C A244448 If both numbers p and p + 2n are primes then x = p+n is a solution to the equation phi(x-n) + sigma(x+n) = phi(x+n) + sigma(x-n). But for these many solutions x, both numbers x-n and x+n are primes.
%C A244448 a(n) is the smallest integer m such that m-n is composite and A051612(m+n) = A051612(m-n) where A051612(n) = sigma(n) - phi(n). - _Michel Marcus_, Mar 20 2020
%H A244448 Michel Marcus, <a href="/A244448/b244448.txt">Table of n, a(n) for n = 0..4501</a> (terms 0..1000 from Jinyuan Wang)
%e A244448 a(1)=153 because 153-1 is composite, phi(153-1)+sigma(153+1) = phi(153+1)+sigma(153-1) and there is no such number less than 153.
%t A244448 a[0]=4;a[n_]:=a[n]=(For[m=n+1,PrimeQ[m-n]||EulerPhi[m-n]+DivisorSigma[1,m+n]!=EulerPhi[m+n]+DivisorSigma[1,m-n],m++];m);
%t A244448 Table[a[n],{n,0,70}]
%o A244448 (PARI) a(n) = {my(m=n+4); while(isprime(m-n) || eulerphi(m+n)+sigma(m-n)!=eulerphi(m-n)+sigma(m+n), m++); m; }
%o A244448 vector(100,n,a(n)) \\ _Derek Orr_, Aug 30 2014
%Y A244448 Cf. A000010 (phi), A000203 (sigma), A051612 (sigma - phi).
%Y A244448 Cf. A244446, A244447, A246628.
%K A244448 nonn
%O A244448 0,1
%A A244448 _Jahangeer Kholdi_ and _Farideh Firoozbakht_, Aug 30 2014