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 A059380 Array of values of Jordan function J_k(n) read by antidiagonals (version 2). 20
 1, 1, 1, 1, 3, 2, 1, 7, 8, 2, 1, 15, 26, 12, 4, 1, 31, 80, 56, 24, 2, 1, 63, 242, 240, 124, 24, 6, 1, 127, 728, 992, 624, 182, 48, 4, 1, 255, 2186, 4032, 3124, 1200, 342, 48, 6, 1, 511, 6560, 16256, 15624, 7502, 2400, 448, 72, 4, 1, 1023, 19682 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 REFERENCES L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 199, #3. R. Sivaramakrishnan, The many facets of Euler's totient. II. Generalizations and analogues, Nieuw Arch. Wisk. (4) 8 (1990), no. 2, 169-187 LINKS Enrique Pérez Herrero, Table of n, a(n) for n = 1..10000 EXAMPLE Array begins: 1, 1, 2, 2, 4, 2, 6, 4, 6, 4, 10, 4, ... 1, 3, 8, 12, 24, 24, 48, 48, 72, 72, ... 1, 7, 26, 56, 124, 182, 342, 448, 702, ... 1, 15, 80, 240, 624, 1200, 2400, 3840, ... MAPLE J := proc(n, k) local i, p, t1, t2; t1 := n^k; for p from 1 to n do if isprime(p) and n mod p = 0 then t1 := t1*(1-p^(-k)); fi; od; t1; end; MATHEMATICA JordanTotient[n_, k_:1]:=DivisorSum[n, #^k*MoebiusMu[n/#]&]/; (n>0)&&IntegerQ[n]; A004736[n_]:=Binomial[Floor[3/2+Sqrt[2*n]], 2]-n+1; A002260[n_]:=n-Binomial[Floor[1/2+Sqrt[2*n]], 2]; A059380[n_]:=JordanTotient[A002260[n], A004736[n]]; (* Enrique Pérez Herrero, Dec 19 2010 *) PROG (PARI) jordantot(n, k)=sumdiv(n, d, d^k*moebius(n/d)); A002260(n)=n-binomial(floor(1/2+sqrt(2*n)), 2); A004736(n)=binomial(floor(3/2+sqrt(2*n)), 2)-n+1; A059380(n)=jordantot(A002260(n), A004736(n)); \\ Enrique Pérez Herrero, Jan 08 2011 CROSSREFS See A059379 and A059380 (triangle of values of J_k(n)), A000010 (J_1), A059376 (J_3), A059377 (J_4), A059378 (J_5). Columns give A000225, A024023, A020522, A024049, A059387, etc. Main diagonal gives A067858. Sequence in context: A161009 A111960 A130462 * A145035 A192020 A171128 Adjacent sequences:  A059377 A059378 A059379 * A059381 A059382 A059383 KEYWORD nonn,tabl AUTHOR N. J. A. Sloane, Jan 28 2001 STATUS approved

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Last modified October 18 14:52 EDT 2019. Contains 328161 sequences. (Running on oeis4.)