A134557 - OEIS

%I #6 Aug 11 2020 11:12:22

%S 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,

%T 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,

%U 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

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

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

%H PlanetMath, <a href="https://planetmath.org/multiplicativeencoding">Multiplicative encoding</a>

%e Triangle begins:

%e {1}

%e {1, 1}

%e {3, 1, 1}

%e {4, 2, 1, 1}

%e {8, 4, 2, 1, 1}

%e {10, 5, 2, 1, 1, 1}

%e {15, 6, 3, 2, 1, 1, 1}

%e {16, 8, 3, 2, 1, 1, 1, 1}

%e 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.

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

%Y Cf. A039716.

%K nonn,tabl

%O 1,4

%A _Alonso del Arte_, Jan 22 2008