OFFSET
1,2
COMMENTS
Column k lists the terms of A000005 interleaved with k - 1 zeros.
Eigensequence of the triangle = A007557; i.e., sequence A007557 shifts to the left upon multiplication by A127170. - Gary W. Adamson, Apr 27 2009
LINKS
Michael De Vlieger, Table of n, a(n) for n = 1..11325 (rows n = 1..150, flattened)
FORMULA
A007429(n) = Sum_{i=1..n} i*a(i).
T(n,k) = A000005(n/k), if k divides n, otherwise 0, with n >= 1 and 1 <= k <= n. - Omar E. Pol, Apr 01 2015
EXAMPLE
First 10 rows of the triangle:
1;
2, 1;
2, 0, 1;
3, 2, 0, 1;
2, 0, 0, 0, 1;
4, 2, 2, 0, 0, 1;
2, 0, 0, 0, 0, 0, 1;
4, 3, 0, 2, 0, 0, 0, 1;
3, 0, 2, 0, 0, 0, 0, 0, 1;
4, 2, 0, 0, 2, 0, 0, 0, 0, 1;
...
MAPLE
T:= (n, k)-> `if`(irem(n, k)=0, numtheory[tau](n/k), 0):
seq(seq(T(n, k), k=1..n), n=1..14); # Alois P. Heinz, Feb 16 2022
MATHEMATICA
Table[Function[D, Table[Count[D, _?(Mod[#, k] == 0 &)], {k, n}]]@ Divisors[n], {n, 12}] // Flatten (* Michael De Vlieger, Feb 16 2022 *)
PROG
(PARI) tabl(nn) = {m = matrix(nn, nn, n, k, if ((n % k) == 0, 1, 0)); m = m^2; for (n=1, nn, for (k=1, n, print1(m[n, k], ", "); ); print(); ); } \\ Michel Marcus, Apr 01 2015
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Gary W. Adamson, Jan 06 2007
EXTENSIONS
8 terms taken from Example section and then corrected in Data section by Omar E. Pol, Mar 30 2015
Extended beyond a(21) by Omar E. Pol, Apr 01 2015
New name (which was a comment dated Mar 30 2015) from Omar E. Pol, Feb 16 2022
STATUS
approved