A262432 - OEIS

%I #16 Mar 24 2017 00:47:58

%S 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,

%T 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,

%U 2,1,2,0,1,1,1,0,1,0,2,1,2,1,2,0,1,1,1,0,1,0,1

%N 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.

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

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

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

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

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

%H Michel Marcus, <a href="/A262432/b262432.txt">Table of n, a(n) for n = 1..5050</a>

%e 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.

%e Triangle starts

%e 1;

%e 1, 1;

%e 1, 1, 1;

%e 1, 1, 1, 1;

%e 1, 1, 1, 1, 1;

%e 2, 1, 1, 1, 1, 0;

%e 2, 1, 1, 1, 1, 0, 1;

%e 2, 1, 1, 1, 1, 0, 1, 1;

%e 2, 1, 1, 1, 1, 0, 1, 1, 1;

%e 2, 1, 1, 1, 2, 0, 1, 1, 1, 0;

%e ...

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

%o (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(););}

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

%K nonn,tabl

%O 1,16

%A _Michel Marcus_, Sep 22 2015