A334990 a(1) = 1 and for any n > 1 with prime factorization Product_{k = 1..m} prime(k)^e_k (where prime(k) denotes the k-th prime number and e_m > 0), a(n) = Product_{k = 1..m-1} prime(k)^(e_k XOR e_{k+1}) (where XOR denotes the bitwise XOR operator).

1, 1, 2, 1, 3, 1, 5, 1, 4, 6, 7, 8, 11, 10, 2, 1, 13, 8, 17, 12, 30, 14, 19, 4, 9, 22, 8, 20, 23, 1, 29, 1, 42, 26, 3, 1, 31, 34, 66, 24, 37, 15, 41, 28, 108, 38, 43, 32, 25, 18, 78, 44, 47, 4, 105, 40, 102, 46, 53, 8, 59, 58, 180, 1, 165, 21, 61, 52, 114, 6

Offset

1,3

Comments

This sequence has similarities with A038554; here we consider prime exponents, there binary digits.

Links

Table of n, a(n) for n=1..70.

Index entries for sequences related to XOR-triangles

Formula

a(n) = 1 iff n belongs to A100778.

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

a(n^k) = a(n)^k for any k >= 0 and any squarefree number n.

a(prime(n+1)) = prime(n).

A006530(a(n)) < A006530(n) for any n > 1.

Prog

(PARI) a(n) = { my (v=1, p=2, e=valuation(n, p)); n/=p^e; forprime (q=p+1, oo, if (n==1, return (v), my (f=valuation(n, q)); n/=q^f; v*=p^bitxor(e, f); [p, e]=[q, f])) }

Crossrefs

Cf. A006530, A038554, A100778.

Sequence in context: A178810 A374237 A319627 * A217668 A119479 A130008

Adjacent sequences: A334987 A334988 A334989 * A334991 A334992 A334993

Keyword

nonn,base

Author

Rémy Sigrist, May 18 2020

Status

approved