Search: id:A059379
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%I A059379
%S A059379 1,1,1,2,3,1,2,8,7,1,4,12,26,15,1,2,24,56,80,31,1,6,24,124,240,
%T A059379 242,63,1,4,48,182,624,992,728,127,1,6,48,342,1200,3124,4032,2186,
%U A059379 255,1,4,72,448,2400,7502,15624,16256,6560,511,1,10,72,702,3840
%N A059379 Array of values of Jordan function J_k(n) read by antidiagonals (version 
               1).
%D A059379 L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 199, #3.
%D A059379 R. Sivaramakrishnan, "The many facets of Euler's totient. II. Generalizations 
               and analogues", Nieuw Arch. Wisk. (4) 8 (1990), no. 2, 169-187.
%F A059379 J_k(n) = sum( d divides n, d^k*mu(n/d)) - Benoit Cloitre (benoit7848c(AT)orange.fr) 
               and Michael Orrison (orrison(AT)math.hmc.edu), Jun 07 2002
%e A059379 Array begins:
%e A059379 1, 1, 2, 2, 4, 2, 6, 4, 6, 4, 10, 4, ...
%e A059379 1, 3, 8, 12, 24, 24, 48, 48, 72, 72, ...
%e A059379 1, 7, 26, 56, 124, 182, 342, 448, 702, ...
%e A059379 1, 15, 80, 240, 624, 1200, 2400, 3840, ...
%p A059379 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;
%Y A059379 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.
%Y A059379 Sequence in context: A158909 A101477 A077887 this_sequence A065487 A025258 
               A118846
%Y A059379 Adjacent sequences: A059376 A059377 A059378 this_sequence A059380 A059381 
               A059382
%K A059379 nonn,tabl
%O A059379 1,4
%A A059379 N. J. A. Sloane (njas(AT)research.att.com), Jan 28 2001

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