1,1

This is to A047999 "Triangle formed by reading Pascal's triangle mod 2" as A007188 "Multiplicative encoding of Pascal triangle: Product p(i+1)^C(n,i)" is to A007318 "Pascal's triangle read by rows." a(2^n) = primorial(2^n) = A002110(A000079(n)). In row(n) the primes with exponent 1 form row(n) of a Sierpinski sieve, so this sequence is a kind of Godelization of a Sierpinski sieve.

a(n) = Prod[i=i..n] p(i+1)^[C(n,i) mod 2]. a(n) = a(n) = Prod[i=1..n] p(i+1)^T(n,i), where T(n,i), are as in A047999 and where Sum_{k>=0} T(n, k) = A001316(n) = 2^A000120(n).

a(1) = 2^T(1,1) = 2^1 = 2.

a(2) = 2^T(2,1) * 3^T(2,2) = 2^1 * 3^1 = 6.

a(3) = 2^T(3,1) * 3^T(3,2) * 5^T(3,3) = 2^1 * 3^0 * 5^1 = 10.

a(4) = 2^T(4,1) * 3^T(4,2) * 5^T(4,3) * 7^T(4,4) = 2^1 * 3^1 * 5^1 * 7^1 = 210.

a(5) = 2^1 * 3^0 * 5^0 * 7^0 * 11^1 = 22.

a(6) = 2^1 * 3^1 * 5^0 * 7^0 * 11^1 * 13^1 = 858.

a(7) = 2^1 * 3^0 * 5^1 * 7^0 * 11^1 * 13^0 * 17^1 = 1870.

a(8) = 2^1 * 3^1 * 5^1 * 7^1 * 11^1 * 13^1 * 17^1 * 19^1 = 9699690.

a(9) = 2^1 * 3^0 * 5^0 * 7^0 * 11^0 * 13^0 * 17^0 * 19^0 * 23^1 = 46.

a(10) = 2^1 * 3^1 * 5^0 * 7^0 * 11^0 * 13^0 * 17^0 * 19^0 * 23^1 * 29^1 = 4002.

a(11) = 2^1 * 3^0 * 5^1 * 7^0 * 11^0 * 13^0 * 17^0 * 19^0 * 23^1 * 29^0 * 31^1 = 7130.

a(12) = 2^1 * 3^1 * 5^1 * 7^1 * 11^0 * 13^0 * 17^0 * 19^0 * 23^1 * 29^1 * 31^1 * 37^1 = 160660290.

a(13) = 2^1 * 3^0 * 5^0 * 7^0 * 11^1 * 13^0 * 17^0 * 19^0 * 23^1 * 29^0 * 31^0 * 37^0 * 41^1 = 20746.

Cf. A000040, A000120, A001316, A007188, A007318, A047999.

Sequence in context: A124621 A065799 A162582 this_sequence A136699 A033710 A123112

Adjacent sequences: A123095 A123096 A123097 this_sequence A123099 A123100 A123101

easy,nonn

Jonathan Vos Post (jvospost3(AT)gmail.com), Nov 05 2006