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

%I A134557 #6 Aug 11 2020 11:12:22
%S A134557 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 A134557 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 A134557 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 A134557 Triangle multiplicatively decoded from A039716, the factorials of the prime numbers, read by rows.
%D A134557 N. J. A. Sloane, The Encyclopedia of Integer Sequences. New York: Academic Press (1995): Fig. M1722, "Multiplicative encoding of a triangular array"
%H A134557 PlanetMath, <a href="https://planetmath.org/multiplicativeencoding">Multiplicative encoding</a>
%e A134557 Triangle begins:
%e A134557 {1}
%e A134557 {1, 1}
%e A134557 {3, 1, 1}
%e A134557 {4, 2, 1, 1}
%e A134557 {8, 4, 2, 1, 1}
%e A134557 {10, 5, 2, 1, 1, 1}
%e A134557 {15, 6, 3, 2, 1, 1, 1}
%e A134557 {16, 8, 3, 2, 1, 1, 1, 1}
%e A134557 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 A134557 ColumnForm[Table[Take[Flatten[FactorInteger[Prime[n]! ]], {2, 2n, 2}], {n, 15}], Center]
%Y A134557 Cf. A039716.
%K A134557 nonn,tabl
%O A134557 1,4
%A A134557 _Alonso del Arte_, Jan 22 2008