A335049 The prime factorization of a(n) corresponds to the left diagonal of the XOR-triangle built from prime factorization of n, with 2-adic valuation of a(n) given by last row.

1, 2, 6, 4, 30, 3, 210, 8, 36, 15, 2310, 24, 30030, 105, 10, 16, 510510, 72, 9699690, 120, 35, 1155, 223092870, 12, 900, 15015, 216, 840, 6469693230, 5, 200560490130, 32, 770, 255255, 21, 9, 7420738134810, 4849845, 5005, 60, 304250263527210, 70

Offset

1,2

Comments

This sequence is a self-inverse permutation of the natural numbers.

This sequence has strong connections with A334727.

Links

Table of n, a(n) for n=1..42.

Index entries for sequences that are permutations of the natural numbers

Index entries for sequences related to XOR-triangles

Formula

a(n) = n iff n is a power of 2.

a(n^2) = a(n)^2.

a(A019565(n)) = A019565(A334727(n)).

A006530(a(n)) = A006530(n).

A071178(a(n)) = A071178(n).

Example

For n = 198:
- 198 = 11^1 * 7^0 * 5^0 * 3^2 * 2^1,
- the corresponding XOR-triangle is:
         1 0 0 2 1
          1 0 2 3
           1 2 1
            3 3
             0
- so a(n) = 11^1 * 7^1 * 5^1 * 3^3 * 2^0 = 10395.

Prog

(PARI) a(n) = {
    my (f=factor(n),
        m=if (#f~==0, 0, primepi(f[#f~, 1])),
        x=vector(m, k, valuation(n, prime(m+1-k))),
        v=1);
    forstep (i=m, 1, -1,
        v*=prime(i)^x[1];
        x=vector(#x-1, k, bitxor(x[k], x[k+1]));
    );
    v
}

Crossrefs

Cf. A006530, A019565, A071178, A334727, A335019.

Sequence in context: A039656 A263326 A226532 * A006233 A164020 A326579

Adjacent sequences: A335046 A335047 A335048 * A335050 A335051 A335052

Keyword

nonn,base

Author

Rémy Sigrist, May 21 2020

Status

approved