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%I #10 Sep 03 2014 21:07:53
%S 25,323,48,34,53,471,58,78,84,76,71,122,64,144,162,118,74,188,106,258,
%T 156,2512,68,254,94,107,132,2326,876,536,154,182,268,468,98,2061,106,
%U 408,264,286,258,1520900,423,618,276,648,579,518,204,708,196,370,164,1088,300,1518,412,3616,158,1226
%N a(n) is the smallest integer m such that m-n is composite and phi(m-n) + sigma(m+n) = 2*m.
%C For each n, a(n)>n and like a(n)-n, a(n)+n is also composite.
%C If both numbers p & p+2n are primes the x=p+n is a solution for the equation phi(x-n)+sigma(x+n)=2x. But for these many solutions x, both x-n & x+n are primes.
%e a(1)=25 because 25-1 is composite, phi(25-1)+sigma(25+1)=2*25 and there is no such number less than 25.
%t a[n_]:=(For[m=n+1, PrimeQ[m-n]||EulerPhi[m-n]+DivisorSigma[1,m+n]!=2m,m++];m);Table[a[n],{n,60}]
%o (PARI)
%o a(n)=m=n+4;while(isprime(m-n)||eulerphi(m-n)+sigma(m+n)!=2*m,m++);m
%o vector(100,n,a(n)) \\ _Derek Orr_, Aug 30 2014
%Y Cf. A000010, A000203, A244447, A244448.
%K nonn
%O 1,1
%A _Jahangeer Kholdi_ and _Farideh Firoozbakht_, Aug 30 2014
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