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

Author

Paul Tek, Jun 10 2013

Keywords

• nonn

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.

Examples

			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.
		

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

Crossrefs

Cf. A006068.

Cf. A226569 (inverse), A067255, A000040.

Programs

Haskell

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

Perl

# See Tek link.