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A234542 Positive integer solutions to sigma(sigma(k) - k - 3)/phi(k - phi(k) + 3) = 3.

%I A234542 #16 Mar 03 2020 08:49:54
%S A234542 15,35,68,95,119,143,155,188,203,280,289,299,323,371,395,611,695,731,
%T A234542 779,791,803,851,899,923,959,995,1055,1139,1146,1199,1355,1369,1379,
%U A234542 1391,1403,1424,1643,1703,1739,1751,1763,1883,1895,1919,2051,2123,2159,2231,2471,2483,2723,2759,2809
%N A234542 Positive integer solutions to sigma(sigma(k) - k - 3)/phi(k - phi(k) + 3) = 3.
%C A234542 If n is the product of a pair of twin primes (A037074), then n is in the sequence (The first few terms of A037074 are: 15, 35, 143, 323, 899, 1763, 3599, ..).  For these numbers, the numerator is equal to 3*sqrt(n + 1) and the denominator (A186749) is equal to sqrt(n + 1), giving 3 as a result.
%H A234542 Amiram Eldar, <a href="/A234542/b234542.txt">Table of n, a(n) for n = 1..10000</a>
%F A234542 Solutions to A000203(A001065(k) - 3)/A000010(A051953(k) + 3) = 3.
%e A234542 119 appears in the sequence since sigma(sigma(119) - 119 - 3)/phi(119 - phi(119) + 3) = sigma(22)/phi(26) = 36/12 = 3.
%p A234542 with(numtheory); A234542:=n->`if`(sigma(sigma(n)-n-3)/phi(n-phi(n)+3)=3,n,NULL); seq(A234542(n), n=1..5000);
%t A234542 Select[Range[1000], DivisorSigma[1, DivisorSigma[1, #] - # - 3]/EulerPhi[# - EulerPhi[#] + 3] == 3 &] (* _Alonso del Arte_, Jan 01 2014 *)
%Y A234542 Cf. A000010, A000203, A001065, A037074, A051953, A186749.
%K A234542 nonn
%O A234542 1,1
%A A234542 _Wesley Ivan Hurt_, Dec 27 2013