A117160 -id:A117160 - cp's OEIS frontend

A117166 Column 1 of triangle A117165 of Shift-Moebius coefficients and so equals the Shift-Moebius transform of [1,0,0,0,...].

1, -1, -2, -1, -2, 1, -1, 3, 0, 4, 4, 5, 1, 7, 6, 5, 4, 6, 3, 5, 3, 2, 5, -3, -5, -1, 2, -7, -6, -13, -9, -14, -12, -22, -12, -25, -23, -26, -21, -35, -27, -38, -27, -43, -32, -47, -34, -51, -46, -52, -33, -53, -35, -58, -41, -56, -39, -54, -39, -61, -45, -53, -24, -46, -23, -44, -20, -41, -14, -32, -12, -22

Offset: 1

Wouter Meeussen and Paul D. Hanna, Mar 05 2006

sign

Equals the self-convolution inverse of A117161, which is the limit of columns of triangle A112682.

Cf. A117165 (triangle), A117167 (column 2), A117168 (column 3), A117169 (row sums), A117161 (inverse), A117160, A112682.

{a(n)=prod(i=0,n, matrix(n,n,r,c,if(r>=c,if((r+n-i)%(c+n-i)==0,moebius((r+n-i)/(c+n-i)),0))))[ n,1]}

A117169 Row sums of triangle A117165 of Shift-Moebius transform coefficients and so equals the Shift-Moebius transform of [1,1,1,...].

Original entry on oeis.org

1, 0, -1, -1, -2, -1, -2, 0, -2, 0, 1, 2, 0, 3, 3, 4, 4, 6, 5, 7, 6, 7, 10, 7, 4, 7, 10, 7, 8, 5, 7, 6, 6, 1, 5, 0, -1, -2, -1, -8, -6, -11, -7, -15, -12, -20, -15, -24, -27, -33, -25, -36, -28, -41, -39, -48, -42, -51, -46, -61, -61, -69, -58, -72, -64, -77, -70, -85, -76, -90, -85, -94, -86, -99, -84, -100

Offset: 1

Wouter Meeussen and Paul D. Hanna, Mar 05 2006

sign

Cf. A117165 (triangle), A117166 (column 1), A117167 (column 2), A117168 (column 3); A117160.

{a(n)=sum(j=1,n,prod(i=0,n+j-1,matrix(n+j-1,n+j-1,r,c,if(r>=c, if((r+n+j-1-i)%(c+n+j-1-i)==0,moebius((r+n+j-1-i)/(c+n+j-1-i)),0))))[n,j])}

A162696 Trajectory of 1 under morphism taking n to sorted divisors of n+1.

Original entry on oeis.org

1, 2, 1, 3, 1, 2, 1, 2, 4, 1, 2, 1, 3, 1, 2, 1, 3, 1, 5, 1, 2, 1, 3, 1, 2, 1, 2, 4, 1, 2, 1, 3, 1, 2, 1, 2, 4, 1, 2, 1, 2, 3, 6, 1, 2, 1, 3, 1, 2, 1, 2, 4, 1, 2, 1, 3, 1, 2, 1, 3, 1, 5, 1, 2, 1, 3, 1, 2, 1, 2, 4, 1, 2, 1, 3, 1, 2, 1, 3, 1, 5, 1, 2, 1, 3, 1, 2, 1, 3, 1, 2, 4, 1, 7, 1, 2, 1, 3, 1, 2, 1, 2, 4, 1, 2

Offset: 1

Franklin T. Adams-Watters, Jul 10 2009

nonn

1 -> 1,2; 2->1,3; 3->1,2,4; ...

			1 -> 1,2 -> 1,2,1,3 -> 1,2,1,3,1,2,1,2,4 -> ...

Index entries for sequences that are fixed points of mappings

Cf. A007001, A001511, A027750, A112682, A117160.

v=[1,2];for(i=2,60,v=concat(v,divisors(v[i]+1)));v

a(A117160(k+1)) = k (this is the first occurrence of k in the sequence). - Rémy Sigrist, Jan 14 2023

cp's OEIS Frontend

A117166 Column 1 of triangle A117165 of Shift-Moebius coefficients and so equals the Shift-Moebius transform of [1,0,0,0,...].

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A117169 Row sums of triangle A117165 of Shift-Moebius transform coefficients and so equals the Shift-Moebius transform of [1,1,1,...].

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Author

Keywords

Crossrefs

Programs

PARI

A162696 Trajectory of 1 under morphism taking n to sorted divisors of n+1.

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