0,1

The maximum (product of b(k)'s + product of c(k)'s) occurs, for n>=2, when {b(k)} = (2,3,4,...n) and {c(k)} = (1). a(1) = 2 because the product over the empty set is defined here as 1.

a(n)<=A060696(n+1) considering the interleaved partition b={2,4,6,..}, c={1,3,5, 7,...}. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jan 10 2007

By partitioning (1,2,3,...8) into {b(k)} and {c(k)} so that {b(k)} = (1,4,6,8) and {c(k)} = (2,3,5,7), then (product of b(k)'s + product of c(k)'s) is minimized. Therefore a(8) = 1*4*6*8 + 2*3*5*7 = 402.

LQprod := proc(S) if nops(S) = 0 then 1 ; else product(S[i], i=1..nops(S)) ; fi ; end: A127180 := proc(n) local S, m, B, b, c, s, res, i ; res := -1 ; S := {} ; for i from 1 to n do S := S union {i} ; od; for m from 0 to n/2 do B := combinat[permute](n, m) ; for i from 1 to nops(B) do b := op(i, B) ; c := S minus convert(b, set) ; s := LQprod(b)+LQprod(c) ; if res < 0 or s < res then res := s ; fi ; od ; od ; RETURN(res) ; end: for n from 1 to 20 do A127180(n) ; od ; - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jan 10 2007

Cf. A127181.

Sequence in context: A080553 A130377 A049873 this_sequence A089540 A080008 A058697

Adjacent sequences: A127177 A127178 A127179 this_sequence A127181 A127182 A127183

nonn

Leroy Quet (qq-quet(AT)mindspring.com), Jan 07 2007

More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jan 10 2007

a(14) and following from Ray Chandler (rayjchandler(AT)sbcglobal.net), Feb 14 2007