A226532 If n = Product_{i>0} prime(i)^e(i), then a(n) = Product_{i>0} prime(i)^(XOR_{j>=i} e(j)), where XOR is bitwise XOR.

1, 2, 6, 4, 30, 3, 210, 8, 36, 15, 2310, 24, 30030, 105, 5, 16, 510510, 72, 9699690, 120, 35, 1155, 223092870, 12, 900, 15015, 216, 840, 6469693230, 10, 200560490130, 32, 385, 255255, 7, 9, 7420738134810, 4849845, 5005, 60, 304250263527210, 70, 13082761331670030, 9240, 1080, 111546435, 614889782588491410

Offset

1,2

Comments

This sequence is a permutation of the natural numbers.

The powers of 2 are the fixed points of this sequence.

a(prime(i)) = A002110(i) for any i > 0.

a(i^2) = a(i)^2 for any i > 0.

a(A019565(n)) = A019565(A006068(n)) for any n >= 0.

Links

Paul Tek, Table of n, a(n) for n = 1..2370

Paul Tek, PERL program for this sequence

Index entries for sequences that are permutations of the natural numbers

Example

a(50) = a(2^1 * 3^0 * 5^2)
      = 2^xor(1,0,2) * 3^xor(0,2) * 5^xor(2)
      = 2^3          * 3^2        * 5^2
      = 1800.

Prog

(Perl) See link.
(Haskell)
import Data.Bits (xor)
a226532 n = product $ zipWith (^)
            a000040_list (scanr1 xor $ a067255_row n :: [Integer])
-- Reinhard Zumkeller, Jun 11 2013

Crossrefs

Cf. A006068.

Cf. A226569 (inverse), A067255, A000040.

Sequence in context: A092399 A039656 A263326 * A335049 A006233 A164020

Adjacent sequences: A226529 A226530 A226531 * A226533 A226534 A226535

Keyword

nonn

Author

Paul Tek, Jun 10 2013

Status

approved