A262432 Regular triangle read by rows: T(n, k) gives the number of times that the denominator of sigma(x,-1) (A017666) is equal to k when x goes from 1 to n.

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 0, 2, 1, 1, 1, 1, 0, 1, 2, 1, 1, 1, 1, 0, 1, 1, 2, 1, 1, 1, 1, 0, 1, 1, 1, 2, 1, 1, 1, 2, 0, 1, 1, 1, 0, 2, 1, 1, 1, 2, 0, 1, 1, 1, 0, 1, 2, 1, 2, 1, 2, 0, 1, 1, 1, 0, 1, 0, 2, 1, 2, 1, 2, 0, 1, 1, 1, 0, 1, 0, 1

Offset: 1

Author

Michel Marcus, Sep 22 2015

Keywords

• nonn
• tabl

Comments

The sum of terms of the n-th row is n.

T(n, n) = 1 when n is in A014567.

T(n, n) = 0 when n is in A069059.

T(n, 1) increases when n is a multiperfect number A007691.

For a given k, the first index n for which T(n,k) = 1 is A162657(k).

Examples

			The first 6 terms of A017666 are 1, 2, 3, 4, 5, 1 where 1 appears twice, 2 to 5 appear once and 6 is absent; giving the 6th row: 2, 1, 1, 1, 1, 0.
Triangle starts
1;
1, 1;
1, 1, 1;
1, 1, 1, 1;
1, 1, 1, 1, 1;
2, 1, 1, 1, 1, 0;
2, 1, 1, 1, 1, 0, 1;
2, 1, 1, 1, 1, 0, 1, 1;
2, 1, 1, 1, 1, 0, 1, 1, 1;
2, 1, 1, 1, 2, 0, 1, 1, 1, 0;
...
		

Links

• Michel Marcus, Table of n, a(n) for n = 1..5050

Crossrefs

Cf. A007691, A014567, A017666, A069059, A162657.

Programs

Mathematica

Table[Length@ Select[Range@ n, Denominator[DivisorSigma[-1, #]] == k &], {n, 13}, {k, n}] // Flatten (* Michael De Vlieger, Sep 22 2015 *)

PARI

tabl(nn) = {vds = vector(nn, n, denominator(sigma(n,-1))); for (n=1, nn, vin = vector(n, k, vds[k]); rown = vector(n, k, #select(x->x==k, vin)); for(k=1, n, print1(rown[k], ", ")); print(););}