A070829 Array showing which primes divide n >= 2.

1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0

Offset: 2

Author

Wolfdieter Lang, May 17 2002

Keywords

• nonn
• easy
• tabf

Comments

In the Kac reference this array is called rho_{p}(n) := 1 if p divides n else 0.

The row length sequence is A061395(n),n>=2: [1,2,1,3,2,4,1,2,3,5,2,6,4,3,...] (the index of the largest prime dividing n). All row entries beyond these numbers are 0, hence they are not shown. The n=1 row would have 0 for all entries.

The column sequences (without leading zeros) give for m>=1 periodic sequences with the period: 1 followed by p(m)-1 zeros. They start with n=p(m) := A000040(m).

Examples

			{1}, {0, 1}, {1}, {0, 0, 1}, {1, 1}, {0, 0, 0, 1}, {1}, {0, 1}, {1, 0, 1}...
Row n=10: {1,0,1} because p(1)=2 and p(3)= 5 divides 10.
		

References

• Mark Kac, A Personal History of the Scottish Book, pp. 17-27, in R. D. Mauldin (ed.), The Scottish Book, Birkhäuser, Boston, Basel, 1981.

Links

• W. Lang, First 32 rows.

Crossrefs

Cf. A067255 (array with multiplicities).

Formula

a(n, m)=1 if p(m), m>=1, divides n>=2, with the prime p(m) := A000040(m), else 0.