A329647 Bitwise-XOR of exponents of prime factors of A108951(n), where A108951 is fully multiplicative with a(prime(i)) = prime(i)# = Product_{i=1..i} A000040(i).

0, 1, 0, 2, 1, 3, 0, 3, 0, 2, 1, 2, 0, 3, 1, 4, 1, 1, 0, 3, 0, 2, 1, 5, 2, 3, 0, 2, 0, 0, 1, 5, 1, 2, 3, 6, 0, 3, 0, 4, 1, 1, 0, 3, 1, 2, 1, 4, 0, 3, 1, 2, 0, 7, 2, 5, 0, 3, 1, 7, 0, 2, 0, 6, 3, 0, 1, 3, 1, 2, 0, 7, 1, 3, 2, 2, 1, 1, 0, 5, 0, 2, 1, 6, 2, 3, 0, 4, 0, 6, 0, 3, 1, 2, 3, 7, 1, 1, 1, 4, 0, 0, 1, 5, 3

Offset

1,4

Comments

Positions of records are: 1, 2, 4, 6, 16, 24, 36, 54, 256, 384, 576, 864, 1296, 1944, 2916, 4374, 65536, ..., conjectured also to be the positions of the first occurrence of each n.

Links

Antti Karttunen, Table of n, a(n) for n = 1..65537

Index entries for sequences computed from indices in prime factorization

Index entries for sequences related to primorial numbers

Formula

a(n) = A268387(A108951(n)).

a(n) <= A329616(n).

Prog

(PARI)
A034386(n) = prod(i=1, primepi(n), prime(i));
A108951(n) = { my(f=factor(n)); prod(i=1, #f~, A034386(f[i, 1])^f[i, 2]) };  \\ From A108951
A268387(n) = if(n>1, fold(bitxor, factor(n)[, 2]), 0);
A329647(n) = A268387(A108951(n));

Crossrefs

Cf. A034386, A108951, A268387, A329615, A329616.

Sequence in context: A127472 A194665 A004563 * A364235 A146094 A098035

Adjacent sequences: A329644 A329645 A329646 * A329648 A329649 A329650

Keyword

nonn

Author

Antti Karttunen, Nov 18 2019

Status

approved