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 A002323 ((2^m - 1) / p) mod p, where p = prime(n) and m = ord(2,p). (Formerly M2223 N0882) 3
 1, 3, 1, 5, 3, 15, 3, 20, 1, 1, 1, 32, 37, 22, 36, 8, 36, 10, 1, 7, 49, 48, 23, 77, 92, 81, 13, 95, 49, 1, 17, 95, 30, 96, 66, 132, 67, 107, 3, 50, 148, 25, 52, 175, 167, 109, 143, 201, 99, 30, 13, 207, 200, 255, 64, 260, 190, 208, 159, 208, 78, 98, 243, 60 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,2 COMMENTS a(n) = 0 if and only if prime(n) is a Wieferich prime (A001220). - Eric M. Schmidt, Feb 23 2015 REFERENCES D. H. Lehmer, Guide to Tables in the Theory of Numbers. Bulletin No. 105, National Research Council, Washington, DC, 1941, pp. 7-10. W. Meißner, Über die Teilbarkeit von 2^p-2 durch das Quadrat der Primzahl p=1093, Sitzungsberichte der Königlich Preußischen Akadamie der Wissenschaften, Berlin, 35 (1913), 663-667. N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence). N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS Eric M. Schmidt, Table of n, a(n) for n = 2..10000 W. Meissner, Über die Teilbarkeit von 2^p-2 durch das Quadrat der Primzahl p = 1093, Sitzungsberichte Königlich Preussischen Akadamie Wissenschaften Berlin, 35 (1913), 663-667. [Annotated scanned copy] EXAMPLE For p = prime(3) = 5, we find that m = 4 is the smallest positive integer for which 2^m - 1 is divisible by p. So a(3) = ((2^4 - 1) / 5) mod 5 = 3. - Eric M. Schmidt, Jun 21 2013 MATHEMATICA Table[p = Prime[n]; Mod[(2^MultiplicativeOrder[2, p] - 1)/p, p], {n, 2, 100}] (* T. D. Noe, Jun 21 2013 *) PROG (Sage) def A002323(n) : p = nth_prime(n); return (2^(Mod(2, p).multiplicative_order()) - 1) // p % p # Eric M. Schmidt, Jun 21 2013 CROSSREFS Cf. A001220, A001917. Sequence in context: A289891 A289094 A171382 * A294640 A200920 A290534 Adjacent sequences: A002320 A002321 A002322 * A002324 A002325 A002326 KEYWORD nonn,easy AUTHOR EXTENSIONS Proper definition added by and more terms from Eric M. Schmidt, Jun 21 2013 STATUS approved

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Last modified December 7 15:01 EST 2022. Contains 358667 sequences. (Running on oeis4.)