A064894 Binary dilution of n. GCD of exponents in binary expansion of n.

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

Offset: 0

Author

Marc LeBrun, Oct 11 2001

Keywords

• base
• easy
• nonn

Comments

All bits of n in positions not divisible by a(n) are zero. Hence n in binary contains blocks of a(n)-1 "diluting" 0's (for n>1). Also for n>1, a(2^n) = a(2^n + 1) = n. For i,j odd, a(ij) = GCD(a(i),a(j)).

Examples

			577 = 2^0 + 2^6 + 2^9, GCD(0,6,9) = 3 = a(577).
		

Links

• Peter Kagey, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A000079, A064895, A064896, A056538.

Programs

Mathematica

A064894[n_] := Apply[GCD, Flatten[Position[Reverse[IntegerDigits[n, 2]], 1]] - 1];
Array[A064894, 100, 0] (* Paolo Xausa, Feb 13 2024 *)

PARI

a(n) = if (n==0, 0, my(ve = select(x->x==1, Vecrev(binary(n)), 1)); gcd(vector(#ve, k, ve[k]-1))); \\ Michel Marcus, Apr 12 2016

Formula

If n = 2^e0 + 2^e1 +... then a(n) = GCD(e0, e1, ...).

a(A064896(n)) = A056538(n)