

A276804


Second column T[.,2] of array T = A255483: T[0,j] = prime(j), T[i+1,j] = T[i,j]*T[i,j+1]/gcd(T[i,j],T[i,j+1])^2, i >= 0, j >= 1.


4



3, 15, 21, 1155, 39, 3315, 5187, 111546435, 87, 13485, 22533, 1575169365, 48633, 6022953885, 12684118629, 961380175077106319535, 183, 61305, 90951, 24466273755, 187941, 88836891585, 157950690807, 133754519645521334494935, 536007, 573342567585
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OFFSET

0,1


COMMENTS

By construction all terms are divisible by 3, and the nth term a(n1) is divisible by prime(n+1). We have a(n)/3 = (1, 5, 7, 385, 13, 1105, 1729, 37182145, 29, 4495, ...). Neither the sequence of primes appearing here, (5, 7, 13, 29, 61, ...), nor its complement in the primes, ([2, 3,] 11, 17, 19, 23, 31, 37, 41, 43, 47, 53, 59, 67, ...), seem to be listed in the OEIS.
This is also the multiplicative encoding of Pascal's triangle in Z_2 (A047999), shifted by prefixing an initial 0 to the nth row; e.g., n=2 => 1,0,1 => 0,1,0,1 => 2^0 * 3^1 * 5^0 * 7^1 = a(2).


LINKS

Table of n, a(n) for n=0..25.


FORMULA

a(n) = A003961(A123098(n)).
a(n) = Prod_{j=0..n} prime(j+2)^(!(nj & j)), where ! is "not" (=0 for nonzero and 1 for zero) and & is bitwise AND.
a(n) = A007913(A267096(n)) = A007913(A252738(n+2)).  Antti Karttunen, Sep 18 2016


PROG

(PARI) A276804(n)=prod(j=0, n, if(bitand(nj, j), 1, prime(j+2)))


CROSSREFS

Cf. A255483 (the square array T), A123098 (first column of T), A003961.
Cf. A007913, A252738, A267096.
Sequence in context: A318134 A087674 A212846 * A009057 A289712 A083795
Adjacent sequences: A276801 A276802 A276803 * A276805 A276806 A276807


KEYWORD

nonn


AUTHOR

M. F. Hasler, Sep 17 2016


STATUS

approved



