A134557 Triangle multiplicatively decoded from A039716, the factorials of the prime numbers, read by rows.

1, 1, 1, 3, 1, 1, 4, 2, 1, 1, 8, 4, 2, 1, 1, 10, 5, 2, 1, 1, 1, 15, 6, 3, 2, 1, 1, 1, 16, 8, 3, 2, 1, 1, 1, 1, 19, 9, 4, 3, 2, 1, 1, 1, 1, 25, 13, 6, 4, 2, 2, 1, 1, 1, 1, 26, 14, 7, 4, 2, 2, 1, 1, 1, 1, 1, 34, 17, 8, 5, 3, 2, 2, 1, 1, 1, 1, 1, 38, 18, 9, 5, 3, 3, 2, 2, 1, 1, 1, 1, 1, 39, 19, 9, 6, 3, 3, 2

Offset: 1

Author

Alonso del Arte, Jan 22 2008

Keywords

• nonn
• tabl

Examples

			Triangle begins:
{1}
{1, 1}
{3, 1, 1}
{4, 2, 1, 1}
{8, 4, 2, 1, 1}
{10, 5, 2, 1, 1, 1}
{15, 6, 3, 2, 1, 1, 1}
{16, 8, 3, 2, 1, 1, 1, 1}
Row 5 of the triangle is 8, 4, 2, 1, 1 because A039716(5) = 39916800 and 39916800 = 2^8 * 3^4 * 5^2 * 7^1 * 11^1.
		

References

• N. J. A. Sloane, The Encyclopedia of Integer Sequences. New York: Academic Press (1995): Fig. M1722, "Multiplicative encoding of a triangular array"

Links

• PlanetMath, Multiplicative encoding

Crossrefs

Cf. A039716.

Programs

Mathematica

ColumnForm[Table[Take[Flatten[FactorInteger[Prime[n]! ]], {2, 2n, 2}], {n, 15}], Center]