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 A174590 a(n) = (k-1)/lambda(k), the index of the n-th Carmichael number k. 4
 7, 23, 48, 22, 47, 5, 45, 21, 44, 163, 342, 162, 43, 31, 1777, 314, 337, 161, 1753, 70, 2868, 1745, 421, 2487, 1363, 159, 39, 645, 950, 67, 198, 1358, 949, 158, 2303, 134, 305, 1692, 1733, 5731, 2794, 7107, 1732, 345, 1689, 2654, 1671, 1829, 947, 1353, 1557 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The index of a Carmichael number k is i(k) = (k-1)/lambda(k). Or, i(k) = (k-1)/lcm(p_1-1,p_2-1,...,p_j-1), where k = p_1*p_2*...*p_j. - Thomas Ordowski, Oct 15 2015 For composite k, lambda(k) divides k-1 iff k is a Carmichael number. - Thomas Ordowski, Oct 23 2015 LINKS Robert Israel, Table of n, a(n) for n = 1..10000 J. M. Chick, Carmichael number variable relations: three-prime Carmichael numbers up to 10^24, arXiv:0711.2915 [math.NT] 2007-2008, Table 1, p. 34. Andrew Granville and Carl Pomerance, Two contradictory conjectures concerning Carmichael numbers, Math. Comp. 71 (2002), no. 238, 883-908. R. G. E. Pinch, Carmichael numbers up to 10^18, April 2006. Richard Pinch, Carmichael Numbers up to 10^20, Abstract, ANTS 7. Richard Pinch, Carmichael Numbers up to 10^20, Poster, ANTS 7. FORMULA a(n) = (A002997(n) - 1) / lambda(A002997(n)). EXAMPLE a(1)= 7 because A002997(1) = 561, and (561 - 1)/lambda(561) = 560/80 = 7. MAPLE with(numtheory) : for n from 2 to 2000000 do: if type(n, prime)=false and issqrfree(n)=true then  x:=factorset(n):n1:=nops(x):ii:=0:for j from 1 to n1 do:if irem(n-1, x[j]-1)=0  then ii:=ii+1:else fi:od:if ii=n1 then z:=(n-1)/lambda(n):printf(`%d, `, z):else fi:fi:od: MATHEMATICA carNums = Select[Range[561, 3 10^6, 2], CompositeQ[#] && Mod[#, CarmichaelLambda[#]] == 1&]; a[n_] := (carNums[[n]] - 1)/CarmichaelLambda[carNums[[n]]]; Array[a, 60] (* Jean-François Alcover, Sep 05 2018 *) PROG (PARI) t(n)=my(f=factor(n)); for(i=1, #f[, 1], if(f[i, 2]>1||(n-1)%(f[i, 1]-1), return(0))); 1; for(n=1, 1e7, if(n%2 && !isprime(n) && t(n) && n>1, print1((n-1)/(lcm(znstar(n)[2])), ", "))) \\ Altug Alkan, Oct 15 2015 CROSSREFS Cf. A002322 (the Carmichael lambda function), A002997, A011773. Sequence in context: A185955 A158035 A101789 * A162290 A180044 A062725 Adjacent sequences:  A174587 A174588 A174589 * A174591 A174592 A174593 KEYWORD nonn AUTHOR Michel Lagneau, Mar 23 2010, Mar 31 2010 EXTENSIONS Edited by Michel Lagneau, Jul 31 2012 Further edits from N. J. A. Sloane, Oct 31 2015 STATUS approved

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Last modified April 14 12:11 EDT 2021. Contains 342949 sequences. (Running on oeis4.)