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

1,4

References

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

Links

Table of n, a(n) for n=1..98.

PlanetMath, Multiplicative encoding

Example

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.

Mathematica

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

Crossrefs

Cf. A039716.

Sequence in context: A023579 A023577 A188139 * A290342 A219842 A351402

Adjacent sequences: A134554 A134555 A134556 * A134558 A134559 A134560

Keyword

nonn,tabl

Author

Alonso del Arte, Jan 22 2008

Status

approved