1,1

J. H. Conway, personal communication.

a(4) = 7 because 2*3*5 = 30 whose divisors are 1, 2, 3, 5, 6, 10, 15, and 30. The closest p and q are 5 and 6 but its difference is 1 so the next closest p and q are 3 and 10 whose difference is 7.

f[n_List] := (a = n; p = Apply[Times, a]; d = Divisors[p]; l = Length[d]; If[l > 2, If[ EvenQ[l], d = Take[d, {l/2 - 1, l/2 + 2 } ]; l = 4, d = Take[d, {l/2 - 0.5, l/2 + 1.5}]; l = 3]]; Switch[l, 2, If[d[[2]] - d[[1]] == 1, AppendTo[a, d[[1]] + d[[2]]], AppendTo[a, d[[2]] - d[[1]]]], 3, AppendTo[a, d[[3]] - d[[1]]], 4, If[d[[3]] - d[[2]] == 1, AppendTo[a, d[[4]] - d[[1]]], AppendTo[a, d[[3]] - d[[2]]]]]; Return[a]); Nest[f, {2}, 15]

(* first do *) Needs["DiscreteMath`Combinatorica`"] (* then *) f[s_List] := Block[{prod = Times @@ s, fwr = Table[ #[[1]], {#[[2]]}] & /@ FactorInteger[Times @@ s] // Flatten, diffmin = Infinity, adiff, p}, len = 2^Length@fwr; Do[p = Times @@ NthSubset[i, fwr]; adiff = Min@Select[{Abs[prod/p - p], Abs[prod/p + p]}, # > 1 &]; If[adiff < diffmin, diffmin = adiff], {i, 2^len}]; Append[s, diffmin]]; Nest[f, {}, 17] - from Robert G. Wilson v Sep 15 2006

Cf. A082125.

Sequence in context: A016114 A053434 A061166 this_sequence A029732 A037950 A105049

Adjacent sequences: A003678 A003679 A003680 this_sequence A003682 A003683 A003684

nonn,hard,nice

njas, Mira Bernstein (mira(AT)math.berkeley.edu)

a(15) from Robert G. Wilson v, Feb 26 1996

a(16) from Naohiro Nomoto (6284968128(AT)geocities.co.jp), Jun 25 2001

a(17) from Robert G. Wilson v Sep 15 2006