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 A007627 Primitive modest numbers. (Formerly M4888) 2
 13, 19, 23, 29, 49, 59, 79, 89, 103, 109, 111, 133, 199, 203, 209, 211, 233, 299, 311, 409, 411, 433, 499, 509, 511, 533, 599, 611, 709, 711, 733, 799, 809, 811, 833, 899, 911, 1003, 1009, 1011, 1027, 1033, 1037, 1099, 1111 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Modest numbers (A054986) are the same but without assuming (a,b) = 1. For given k, (see FORMULA section) b's are divisors of (10^k - 1), and a's are coprime with b, number of pairs (a,b) is Sum_{i=1..m} phi(b_i) - 1 where b_i are divisors of (10^k - 1), m = d(10^k - 1) the number of divisors of n (A000005), and phi is Euler totient function (A000010). E.g., for k = 1: b = 1, 3, 9, and pairs of (a,b) are: (1,3), (2,3), (1,9), (2,9), (4,9), (5,9), (7,9), and (8,9) - a total of 8 pairs. - Zak Seidov, Mar 22 2012 REFERENCES Problem 1291, J. Rec. Math., 17 (No.2, 1984), 140-141. N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS Reinhard Zumkeller, Table of n, a(n) for n = 1..10000 H. Havermann, Modest numbers, J. Recreational Mathematics, 17.2 (1984), 140-141. (Annotated scanned copy) FORMULA n = a*10^k + b such that (a, b)=1, n == a (mod b), a < b < 10^k. PROG (Haskell) import Data.List (inits, tails) a007627 n = a007627_list !! (n-1) a007627_list = filter modest' [1..] where    modest' x = or \$ zipWith m                (map read \$ (init \$ tail \$ inits \$ show x) :: [Integer])                (map read \$ (tail \$ init \$ tails \$ show x) :: [Integer])       where m u v = u < v && (x - u) `mod` v == 0 && gcd u v == 1 -- Reinhard Zumkeller, Mar 27 2011 CROSSREFS Cf. A054986, A055018. Sequence in context: A191020 A180545 A113017 * A180525 A257590 A121877 Adjacent sequences:  A007624 A007625 A007626 * A007628 A007629 A007630 KEYWORD nonn,easy,base AUTHOR STATUS approved

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Last modified October 16 03:37 EDT 2019. Contains 328040 sequences. (Running on oeis4.)