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 A033553 3-Knödel numbers or D-numbers: numbers n > 3 such that n | k^(n-2)-k for all k with gcd(k, n) = 1. 20
 9, 15, 21, 33, 39, 51, 57, 63, 69, 87, 93, 111, 123, 129, 141, 159, 177, 183, 195, 201, 213, 219, 237, 249, 267, 291, 303, 309, 315, 321, 327, 339, 381, 393, 399, 411, 417, 447, 453, 471, 489, 501, 519, 537, 543, 573, 579, 591, 597, 633, 669, 681, 687, 693, 699, 717, 723, 753, 771, 789, 807, 813, 819 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS From Max Alekseyev, Oct 03 2016: (Start) Also, composite numbers n such that A000010(p^k)=(p-1)*p^(k-1) divides n-3 for every prime power p^k dividing n (cf. A002997). Properties: (i) All terms are odd. (ii) A prime power p^k with k>1 may divide a term only if p=3 and k=2. (iii) Many terms are divisible by 3. The first term not divisible by 3 is a(2000) = 50963 (cf. A277344). (End) All terms satisfy the congruence 2^n == 8 (mod n) and thus belong to A015922. Sequence a(n)/3 is nearly identical to A106317, which does not contain the terms 399/3=133 and 195/3=65. - Gary Detlefs, May 28 2014; corrected by Max Alekseyev, Oct 03 2016 Numbers n > 3 such that A002322(n) divides n-3. - Thomas Ordowski, Jul 15 2017 LINKS R. J. Mathar and Michael De Vlieger, Table of n, a(n) for n = 1..10000 (First 489 terms from R. J. Mathar). John H. Castillo and Jhony Fernando Caranguay Mainguez, The set of k-units modulo n, arXiv:1708.06812 [math.NT], 2017. Eric Weisstein's World of Mathematics, D-Number. Eric Weisstein's World of Mathematics, Knödel Numbers. MAPLE with(numtheory); knodel:=proc(i, k) local a, n, ok; for n from k+1 to i do   ok:=1;   for a from 1 to n do      if gcd(a, n)=1 then  if (a^(n-k) mod n)<>1 then ok:=0; break; fi; fi;   od;   if ok=1 then print(n); fi; od; end: knodel(1000, 3) # Paolo P. Lava, Feb 24 2012 MATHEMATICA Select[Range[4, 10^3], Divisible[# - 3, CarmichaelLambda[#]] &] (* Michael De Vlieger, Jul 15 2017 *) PROG (PARI) { isA033553(n) = my(p=factor(n)); for(i=1, matsize(p)[1], if( (n-3)%eulerphi(p[i, 1]^p[i, 2]), return(0)); ); 1; } \\ Max Alekseyev, Oct 04 2016 CROSSREFS Cf. A002997, A050990, A050992, A050993, A208154-A208158, A277344. Sequence in context: A175626 A096788 A050991 * A020192 A241809 A063174 Adjacent sequences:  A033550 A033551 A033552 * A033554 A033555 A033556 KEYWORD nonn AUTHOR EXTENSIONS Edited by N. J. A. Sloane, May 07 2007 STATUS approved

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Last modified October 15 22:25 EDT 2019. Contains 328038 sequences. (Running on oeis4.)