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 A252911 Irregular triangular array read by rows: T(n,k) is the number of elements in the multiplicative group of integers modulo n that have order k, n>=1, 1<=k<=A002322(n). 1
 1, 1, 1, 1, 1, 1, 1, 1, 0, 2, 1, 1, 1, 1, 2, 0, 0, 2, 1, 3, 1, 1, 2, 0, 0, 2, 1, 1, 0, 2, 1, 1, 0, 0, 4, 0, 0, 0, 0, 4, 1, 3, 1, 1, 2, 2, 0, 2, 0, 0, 0, 0, 0, 4, 1, 1, 2, 0, 0, 2, 1, 3, 0, 4, 1, 3, 0, 4, 1, 1, 0, 2, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 8, 1, 1, 2, 0, 0, 2, 1, 1, 2, 0, 0, 2, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 6, 1, 3, 0, 4 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,10 COMMENTS Row sums are A000010. Column 2 = A155828(n) = A060594(n) - 1. LINKS Alois P. Heinz, Rows n = 1..250, flattened Eric Weisstein's World of Mathematics, Modulo Multiplication Group. EXAMPLE 1; 1; 1, 1; 1, 1; 1, 1, 0, 2; 1, 1; 1, 1, 2, 0, 0, 2; 1, 3; 1, 1, 2, 0, 0, 2; 1, 1, 0, 2; 1, 1, 0, 0, 4, 0, 0, 0, 0, 4; 1, 3; 1, 1, 2, 2, 0, 2, 0, 0, 0, 0, 0, 4; 1, 1, 2, 0, 0, 2; 1, 3, 0, 4; T(15,2)=3 because the elements 4, 11, and 14 have order 2 in the modulo multiplication group (Z/15Z)*. We observe that 4^2, 11^2, and 14^2 are congruent to 1 mod 15. MAPLE with(numtheory): T:= n-> `if`(n=1, 1, (p-> seq(coeff(p, x, j), j=1..degree(p)))(          add(`if`(igcd(n, i)>1, 0, x^order(i, n)), i=1..n-1))): seq(T(n), n=1..30);  # Alois P. Heinz, Dec 30 2014 MATHEMATICA Table[Table[    Count[Table[      MultiplicativeOrder[a, n], {a,       Select[Range[n], GCD[#, n] == 1 &]}], k], {k, 1,     CarmichaelLambda[n]}], {n, 1, 20}] // Grid CROSSREFS Cf. A000010, A002322, A054522, A060594, A155828. Sequence in context: A154243 A326698 A299432 * A176820 A343776 A328384 Adjacent sequences:  A252908 A252909 A252910 * A252912 A252913 A252914 KEYWORD nonn,tabf AUTHOR Geoffrey Critzer, Dec 24 2014 STATUS approved

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Last modified September 22 19:36 EDT 2021. Contains 347608 sequences. (Running on oeis4.)