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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). 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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

Table of n, a(n) for n=1..48.

Eric Weisstein's World of Mathematics, Poulet Number

CROSSREFS

Cf. A001567.

Sequence in context: A103281 A266173 A057400 * A033416 A252715 A050277

Adjacent sequences:  A216401 A216402 A216403 * A216405 A216406 A216407

KEYWORD

nonn

AUTHOR

Marius Coman, Sep 06 2012

STATUS

approved

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Last modified October 18 18:47 EDT 2021. Contains 348068 sequences. (Running on oeis4.)