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A059380 Array of values of Jordan function J_k(n) read by antidiagonals (version 2). 16
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 February 25 22:18 EST 2018. Contains 299662 sequences. (Running on oeis4.)