A127562 a(1)=1. a(2)=2. For n>=3, a(n) is the smallest positive integer not occurring earlier in the sequence such that (Sum_{k=1..n} a(k)) divides Product_{j=1..n} a(j).
1, 2, 3, 6, 4, 8, 12, 18, 10, 16, 20, 25, 19, 27, 9, 36, 24, 30, 15, 35, 22, 33, 5, 38, 14, 43, 11, 26, 13, 7, 28, 34, 31, 21, 17, 23, 29, 39, 44, 42, 40, 32, 45, 51, 37, 47, 48, 50, 52, 46, 56, 60, 41, 55, 54, 58, 53, 57, 49, 62, 59, 61, 63, 64, 65, 69, 66, 70, 68, 73, 71, 77, 67
Offset: 1
Keywords
Examples
a(1)+a(2)+a(3)+a(4)+a(5)+a(6) = 1+2+3+6+4+8 = 24. a(1)*a(2)*a(3)*a(4)*a(5)*a(6) = 1152. And 24 divides 1152. Had a(6) been any of the positive integers which are < 8 and do not occur earlier in the sequence (i.e., had it been 5 or 7), then the sum of the first 6 terms of the sequence would not have divided the product of the first 6 terms.
Links
- Ivan Neretin, Table of n, a(n) for n = 1..1000
Programs
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Mathematica
f[l_List] := Block[{k = 1, s = Plus @@ l, p = Times @@ l},While[MemberQ[l, k] || Mod[k*p, k + s] > 0, k++ ];Append[l, k]];Nest[f, {1, 2}, 75] (* Ray Chandler, Jan 22 2007 *)
Extensions
Extended by Ray Chandler, Jan 22 2007
Comments