Search: id:A060186
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%I A060186
%S A060186 1,0,1,0,5,1,5,2,9,3,9,2,14,1,15,10,15,7,11,14,10,26,20,28,2,41,5,63,21,
%T A060186 82,5,91,49,122,46,139,84,165,74,240,147,242,142,290,217,333,189,378,
%U A060186 284,463,290,508,408,560,377
%V A060186 1,0,1,0,5,-1,5,-2,9,3,9,-2,14,-1,15,10,15,7,11,14,10,26,20,28,2,41,-5,
               63,-21,82,-5,91,
%W A060186 -49,122,-46,139,-84,165,-74,240,-147,242,-142,290,-217,333,-189,378,-284,
               463,-290,508,
%X A060186 -408,560,-377
%N A060186 Generalized sum of divisors function: third diagonal of A060184.
%D A060186 P. A. MacMahon, Divisors of numbers and their continuations in the theory 
               of partitions, Proc. London Math. Soc., (2) 19 (1919), 75-113; Coll. 
               Papers II, pp. 303-341.
%F A060186 G.f.: (t(1)^3-3*t(1)*t(2)+2*t(3))/6 where t(i) = Sum((x^n/(1+x^(n)))^i,
               n=1..inf), i=1..3. - Vladeta Jovovic (vladeta(AT)eunet.rs), Sep 20 
               2007
%p A060186 mufact := proc(k,sumax) local res,c,i,j,isord,s ; res := [] ; for s from 
               k*(k+1)/2 to sumax do c := combinat[composition](s,k) ; for j from 
               1 to nops(c) do isord := true ; for i from 2 to nops(op(j,c)) do 
               if op(i,op(j,c))<= op(i-1,op(j,c)) then isord := false ; fi ; od 
               ; if isord then res := [op(res),op(j,c)] ; fi ; od ; od ; RETURN(res) 
               ; end: qm := proc(gfpart,n) local f,i ; f := q^add(op(i,gfpart),i=1..nops(gfpart)) 
               ; for i from 1 to nops(gfpart) do f := taylor(f/(1+q^op(i,gfpart)),
               q=0,n+1) ; od ; RETURN(f) ; end: A060186 := proc(n) local k,ms,gf,
               gfpart,i ; k := 3 ; ms := mufact(k,n) ; gf := 0; for i from 1 to 
               nops(ms) do gfpart := op(i,ms) ; gf := taylor(gf+qm(gfpart,n),q=0,
               n+1) ; od ; RETURN(gf) ; end: nmax := 60 : a := A060186(nmax) : for 
               n from 6 to nmax do printf("%d, ",coeftayl(a,q=0,n)) ; od ; - R. 
               J. Mathar (mathar(AT)strw.leidenuniv.nl), Jun 26 2007
%Y A060186 Sequence in context: A050340 A021955 A055191 this_sequence A122002 A073226 
               A021198
%Y A060186 Adjacent sequences: A060183 A060184 A060185 this_sequence A060187 A060188 
               A060189
%K A060186 easy,more,sign
%O A060186 3,5
%A A060186 N. J. A. Sloane (njas(AT)research.att.com), Mar 19 2001
%E A060186 More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jun 26 2007

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