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A059380 Array of values of Jordan function J_k(n) read by antidiagonals (version 2). 22
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 A359413 A192020
KEYWORD
nonn,tabl
AUTHOR
N. J. A. Sloane, Jan 28 2001
STATUS
approved

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Last modified March 18 22:56 EDT 2024. Contains 370952 sequences. (Running on oeis4.)