

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 to n) a(k)) divides product{j=1 to n} a(j).


4



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
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OFFSET

1,2


COMMENTS

Is this a permutation of the positive integers?


LINKS

Ivan Neretin, Table of n, a(n) for n = 1..1000


EXAMPLE

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 are not occurring earlier in the sequence (ie, had 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.


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 *)


CROSSREFS

Cf. A127563, A127564.
Sequence in context: A109890 A086537 A212486 * A096113 A110797 A083872
Adjacent sequences: A127559 A127560 A127561 * A127563 A127564 A127565


KEYWORD

nonn


AUTHOR

Leroy Quet, Jan 18 2007


EXTENSIONS

Extended by Ray Chandler, Jan 22 2007


STATUS

approved



