A378888 a(n) = gcd(n, A007814(n)).

1, 1, 3, 2, 5, 1, 7, 1, 9, 1, 11, 2, 13, 1, 15, 4, 17, 1, 19, 2, 21, 1, 23, 3, 25, 1, 27, 2, 29, 1, 31, 1, 33, 1, 35, 2, 37, 1, 39, 1, 41, 1, 43, 2, 45, 1, 47, 4, 49, 1, 51, 2, 53, 1, 55, 1, 57, 1, 59, 2, 61, 1, 63, 2, 65, 1, 67, 2, 69, 1, 71, 3, 73, 1, 75, 2

Offset

1,3

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Formula

a(2*n-1) = 2*n-1.

a(2*n) = A378887(n).

Sum_{k=1..n} a(k) ~ n^2/4 + c*n/2, where c = 1.62390224555724623579... is the asymptotic mean of A378887 (see the Formula section of A378887).

Mathematica

a[n_] := GCD[n, IntegerExponent[n, 2]]; Array[a, 100]

Prog

(PARI) a(n) = gcd(n, valuation(n, 2));

Crossrefs

Cf. A007814, A378887 (even bisection).

Sequence in context: A099643 A224344 A113260 * A051543 A265574 A129538

Adjacent sequences: A378885 A378886 A378887 * A378889 A378890 A378891

Keyword

nonn,easy,new

Author

Amiram Eldar, Dec 10 2024

Status

approved