A127644 a(1)=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).

3, 6, 9, 18, 12, 16, 8, 24, 32, 34, 30, 48, 15, 1, 14, 2, 17, 11, 20, 4, 26, 7, 21, 22, 5, 27, 10, 13, 25, 40, 19, 28, 33, 37, 23, 42, 38, 44, 35, 31, 41, 29, 46, 49, 39, 50, 36, 43, 47, 45, 51, 54, 55, 53, 52, 56, 57, 62, 61, 60, 64, 68, 67, 58, 63, 70, 69, 71, 65, 77, 66, 72

Offset: 1

Author

Leroy Quet, Jan 22 2007

Keywords

• nonn

Comments

Is this a permutation of the positive integers? According to Hans Havermann, this sequence matches sequence A127562 beginning with the 104th term of each. Unlike sequence A127562, the sum of the first n terms of this sequence divides the product of the first n terms for every positive integer n.

Crossrefs

Cf. A127562, A127645, A127646.

Programs

Maple

N:= 1000: # to get a(1) to a(m-1) where a(m) is the first term > N
a[1]:= 3:
R:= {$1..N} minus {3}:
P:= 3:
S:= 3:
success:= true:
for n from 2 while success and R <> {} do
   success := false;
   for r in R do
     if type((P*r)/(S+r),integer) then
        a[n]:= r;
        nmax:= n;
        R:= R minus {r};
        success:= true;
        P:= P * r;
        S:= S + r;
        break
     fi
   od:
od:
seq(a[i],i=1..nmax); # Robert Israel, Dec 13 2014

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, {3}, 75] (* Ray Chandler, Jan 22 2007 *)

PARI

v=[3];print1(3,", ");n=1;while(n<100,p=prod(i=1,#v,v[i]);if(p*n\(vecsum(v)+n)==p*n/(vecsum(v)+n)&&!vecsearch(vecsort(v),n),v=concat(v,n);print1(n,", ");n=0);n++) \\ Derek Orr, Dec 13 2014

Extensions

Extended by Ray Chandler, Jan 22 2007