The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A115948 a(n) = (2^(semiprime(n)-1)) modulo (semiprime(n)^2). 0
 8, 32, 13, 12, 156, 184, 319, 464, 341, 496, 301, 308, 9, 952, 472, 508, 1191, 922, 2359, 688, 1800, 2668, 2291, 3109, 2888, 4860, 412, 4691, 604, 2875, 4523, 2236, 3856, 5659, 2016, 8662, 3259, 8852, 13239, 6953, 1344, 6277, 7357, 2857, 11660, 18193 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Wieferich function of semiprimes. This appears in the search for the semiprime analogy to A001220 Wieferich primes p: p^2 divides 2^(p-1) - 1. That is, the Wieferich function W(p) of primes p is W(p) = 2^(p-1) modulo p^2 and a (rare!) Wieferich prime (A001220) is one such that W(p) = 1. The current sequence is W(semiprime(n)). Any semiprime s for which W(s) = 1 would be a "Wieferich semiprime." This is also related to Fermat's "little theorem" that for any odd prime p we have 2^(p-1) == 1 modulo p. Such a "Wieferich semiprime" would be a special case of a "Wieferich pseudoprime", i.e. it would be a composite integer that is one more than a term in A240719 and has two prime factors. - Felix Fröhlich, Jul 16 2014 REFERENCES R. Crandall and C. Pomerance, Prime Numbers: A Computational Perspective, Springer, NY, 2001; see p. 28. R. K. Guy, Unsolved Problems in Number Theory, A3. G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, 5th ed., Oxford Univ. Press, 1979, th. 91. LINKS FORMULA a(n) = (2^(A001358(n)-1)) modulo (A001358(n)^2). MATHEMATICA PowerMod[2, # - 1, #^2] & /@ Select[ Range@141, Plus @@ Last /@ FactorInteger@# == 2 &] (* Robert G. Wilson v *) CROSSREFS Cf. A001220, A001358. Sequence in context: A102275 A299448 A300086 * A322056 A059880 A144096 Adjacent sequences:  A115945 A115946 A115947 * A115949 A115950 A115951 KEYWORD easy,nonn AUTHOR Jonathan Vos Post, Mar 14 2006 EXTENSIONS More terms from Robert G. Wilson v, Mar 14 2006 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified October 18 01:39 EDT 2021. Contains 348065 sequences. (Running on oeis4.)