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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.

%I A262432 #16 Mar 24 2017 00:47:58
%S A262432 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 A262432 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 A262432 2,1,2,0,1,1,1,0,1,0,2,1,2,1,2,0,1,1,1,0,1,0,1
%N 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.
%C A262432 The sum of terms of the n-th row is n.
%C A262432 T(n, n) = 1 when n is in A014567.
%C A262432 T(n, n) = 0 when n is in A069059.
%C A262432 T(n, 1) increases when n is a multiperfect number A007691.
%C A262432 For a given k, the first index n for which T(n,k) = 1 is A162657(k).
%H A262432 Michel Marcus, <a href="/A262432/b262432.txt">Table of n, a(n) for n = 1..5050</a>
%e A262432 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 A262432 Triangle starts
%e A262432 1;
%e A262432 1, 1;
%e A262432 1, 1, 1;
%e A262432 1, 1, 1, 1;
%e A262432 1, 1, 1, 1, 1;
%e A262432 2, 1, 1, 1, 1, 0;
%e A262432 2, 1, 1, 1, 1, 0, 1;
%e A262432 2, 1, 1, 1, 1, 0, 1, 1;
%e A262432 2, 1, 1, 1, 1, 0, 1, 1, 1;
%e A262432 2, 1, 1, 1, 2, 0, 1, 1, 1, 0;
%e A262432 ...
%t A262432 Table[Length@ Select[Range@ n, Denominator[DivisorSigma[-1, #]] == k &], {n, 13}, {k, n}] // Flatten (* _Michael De Vlieger_, Sep 22 2015 *)
%o A262432 (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 A262432 Cf. A007691, A014567, A017666, A069059, A162657.
%K A262432 nonn,tabl
%O A262432 1,16
%A A262432 _Michel Marcus_, Sep 22 2015