A216404 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).

96, 36, 132, 126, 740, 280, 384, 360, 90, 1406, 224, 570, 2090, 774, 96, 608, 1408, 168, 4070, 4266, 516, 680, 2656, 1110, 360, 252, 1064, 2340, 672, 7436, 1368, 1184, 1806, 660, 9506, 3384, 252, 11858, 4448, 8246, 4648, 720, 5310, 16058, 8008, 5676, 3630, 17910

Offset: 1

Author

Marius Coman, Sep 06 2012

Keywords

• nonn

Comments

It is notable how many primes are obtained if we add or subtract 1 from these numbers.

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).

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).

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.

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).

Links

• Eric Weisstein's World of Mathematics, Poulet Number

Crossrefs

Cf. A001567.