A210208 Triangle read by rows in which row n lists the divisors of n that are prime powers, A000961.

1, 1, 2, 1, 3, 1, 2, 4, 1, 5, 1, 2, 3, 1, 7, 1, 2, 4, 8, 1, 3, 9, 1, 2, 5, 1, 11, 1, 2, 3, 4, 1, 13, 1, 2, 7, 1, 3, 5, 1, 2, 4, 8, 16, 1, 17, 1, 2, 3, 9, 1, 19, 1, 2, 4, 5, 1, 3, 7, 1, 2, 11, 1, 23, 1, 2, 3, 4, 8, 1, 5, 25, 1, 2, 13, 1, 3, 9, 27, 1, 2, 4, 7

Offset: 1

Author

Reinhard Zumkeller, Mar 18 2012

Keywords

• nonn
• tabf

Comments

{T(n,k): k = 1..A073093(n)} subset of {A027750(n,k): k = 1..A000005(n)} for all n.

Examples

			Table begins:
  1;
  1, 2;
  1, 3;
  1, 2, 4;
  1, 5;
  1, 2, 3;
  1, 7;
  1, 2, 4, 8;
  1, 3, 9;
  1, 2, 5;
  1, 11;
  1, 2, 3, 4; - _Geoffrey Critzer_, Feb 08 2015
		

Links

• Reinhard Zumkeller, Rows n=1..5000 of triangle, flattened
• Eric Weisstein's World of Mathematics, Divisor.

Crossrefs

Cf. A073093 (row lengths), A023888 (row sums), A034699 (row maxima), A183091 (row products).

Cf. A000005, A010055, A027750, A141809.

Programs

Haskell

a210208 n k = a210208_tabf !! (n-1) !! (n-1)
a210208_row n = a210208_tabf !! (n-1)
a210208_tabf = map (filter ((== 1) . a010055)) a027750_tabf

Mathematica

Table[Prepend[Select[Divisors[n], PrimeNu[#] == 1 &], 1], {n, 1, 10}]//Grid (* Geoffrey Critzer, Feb 08 2015 *)

PARI

row(n) = select(x -> omega(x) < 2, divisors(n)); \\ Amiram Eldar, May 02 2025

Formula

A034699(n) = T(n,A073093(n)) = maximum of n-th row.