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%I #11 Sep 04 2017 23:22:53
%S 15,35,56,72,78,84,123,143,165,323,543,627,678,728,814,836,899,1350,
%T 1484,1535,1683,1763,1846,2296,2967,3288,3444,3599,3784,4103,4620,
%U 5084,5183,5964,6580,6693,6820,7150,7626,7806,9096
%N Numbers k such that phi(k) + 1 = x^2 and sigma(k) + 1 = y^2 for some x and y.
%H Harry J. Smith, <a href="/A063532/b063532.txt">Table of n, a(n) for n = 1..500</a>
%e If k = p(p+2) is a product of twin primes then phi(k) + 1 = p^2, sigma(k) + 1 = (p+2)^2, so k is in the sequence, A037074 a proper subset. There are many solutions not of this form, such as 72, 123, and 165.
%o (PARI) { n=0; for (a=1, 10^9, if (issquare(eulerphi(a) + 1) && issquare(sigma(a) + 1), write("b063532.txt", n++, " ", a); if (n==500, break)) ) } \\ _Harry J. Smith_, Aug 25 2009
%Y Cf. A000010, A000203, A037074.
%K nonn
%O 1,1
%A _Labos Elemer_, Aug 02 2001
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