A056135 -id:A056135 - cp's OEIS frontend

A086480 Erroneous version of A056135.

4, 8, 12, 1, 125, 24, 343, 2, 1, 40, 1331, 3, 2197, 56, 3375

Offset: 0

dead

A056134 Smallest positive integer which is the geometric mean of n and an integer other than n.

2, 4, 6, 2, 10, 12, 14, 4, 3, 20, 22, 6, 26, 28, 30, 4, 34, 6, 38, 10, 42, 44, 46, 12, 5, 52, 9, 14, 58, 60, 62, 8, 66, 68, 70, 6, 74, 76, 78, 20, 82, 84, 86, 22, 15, 92, 94, 12, 7, 10, 102, 26, 106, 18, 110, 28, 114, 116, 118, 30, 122, 124, 21, 8, 130, 132, 134, 34, 138, 140

Offset: 1

Henry Bottomley, Jun 13 2000

a(n)=sqrt(n*A056135(n)). If n is squarefree then a(n)=2n, otherwise a(n)=A019554(n)

A159586 a(n) is the smallest number not yet used such that n*a(n) is a square, but n != a(n).

Original entry on oeis.org

4, 8, 12, 1, 20, 24, 28, 2, 16, 40, 44, 3, 52, 56, 60, 9, 68, 32, 76, 5, 84, 88, 92, 6, 36, 104, 48, 7, 116, 120, 124, 18, 132, 136, 140, 25, 148, 152, 156, 10, 164, 168, 172, 11, 80, 184, 188, 27, 64, 72, 204, 13, 212, 96, 220, 14, 228, 232, 236, 15, 244, 248, 112, 49

Offset: 1

Franklin T. Adams-Watters, Apr 16 2009

nonn

This is a self-inverse permutation of the positive integers.
Equivalently, the geometric mean of n and a(n) is an integer.
If n is squarefree, a(n) = 4n.

Cf. A159253, A056135.

invect(v,n,x)=for(i=1,n,if(v[i]==x,return(1)));0
nextnew(v,n)=local(k);k=1;while(!R(n,k)||invect(v,n-1,k),k++);k
newvect(n)=local(v);v=vector(n);for(k=1,n,v[k]=nextnew(v,k));v
R(n,m)=issquare(n*m)&&n!=m
newvect(80)

cp's OEIS Frontend

A086480 Erroneous version of A056135.

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A056134 Smallest positive integer which is the geometric mean of n and an integer other than n.

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A159586 a(n) is the smallest number not yet used such that n*a(n) is a square, but n != a(n).

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