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%I #19 Mar 04 2018 17:47:11
%S 96,36,132,126,740,280,384,360,90,1406,224,570,2090,774,96,608,1408,
%T 168,4070,4266,516,680,2656,1110,360,252,1064,2340,672,7436,1368,1184,
%U 1806,660,9506,3384,252,11858,4448,8246,4648,720,5310,16058,8008,5676,3630,17910
%N a(n) = lcm((d1 + 1), (d2 + 1), ..., (dk + 1)), where d1, d2, ..., dk are the prime factors of the n-th Fermat pseudoprime to base 2, A001567(n).
%C It is notable how many primes are obtained if we add or subtract 1 from these numbers.
%C Primes obtained by adding 1 and the corresponding Fermat pseudoprime in the brackets: 97(341), 37(561), 127(1105), 281(1729), 571(3277), 97(4371), 1409(5461), 2657(10261), 2341(13747), 673(13981), 661(18705), 46499(30121), 8009(31621), 3631(34945), 17911(35333).
%C Primes obtained by subtracting 1 and the corresponding Fermat pseudoprime in the brackets: 131(645), 739(1387), 383(1905), 359(2047), 89(2465), 223(2821), 569(3277), 2089(4033), 773(4369), 607(4681), 167(6601), 1109(10585), 359(11305), 251(12801), 1063(13741), 2339(13747), 1367(15709), 659(18705), 251(23001), 4447(25761), 719(30889), 5309(31417), 160479(31609), 17909(35333).
%C Numbers from sequence which do not lead to a prime number adding or subtracting 1 (and the corresponding Fermat pseudoprimes to base 2 in the bracketts): 1406(2701), 4070(7957), 4266(8321), 516(8481), 680(8911), 7436(14491), 1184(15841), 1806(16705), 9506(18721), 3384(19951), 11858(23377), 8246(29341), 5676(33153). Interesting analogies can be found between these "exceptions": subtracting 1 from the ones of the form 10*k + 6 often yields semiprimes, etc.
%C There are probably many other interesting utilities for the function from the sequence above as for the function a(n) = lcm(d1-1, d2-1, ..., dk-1), where d1, d2, ..., dk are the prime factors of the n-th Fermat pseudoprime to base 2 A001567(n).
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PouletNumber.html">Poulet Number</a>
%Y Cf. A001567.
%K nonn
%O 1,1
%A _Marius Coman_, Sep 06 2012
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