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Binary dilution of n. GCD of exponents in binary expansion of n.
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%I #21 Feb 13 2024 09:57:39

%S 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,

%T 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,

%U 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

%N Binary dilution of n. GCD of exponents in binary expansion of n.

%C 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)).

%H Peter Kagey, <a href="/A064894/b064894.txt">Table of n, a(n) for n = 0..10000</a>

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

%F a(A064896(n)) = A056538(n)

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

%t A064894[n_] := Apply[GCD, Flatten[Position[Reverse[IntegerDigits[n, 2]], 1]] - 1];

%t Array[A064894, 100, 0] (* _Paolo Xausa_, Feb 13 2024 *)

%o (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

%Y Cf. A000079, A064895, A064896, A056538.

%K base,easy,nonn

%O 0,5

%A _Marc LeBrun_, Oct 11 2001