cp's OEIS Frontend

A064895 Binary concentration of n. Replace 2^e_k with 2^(e_k/g(n)) in binary expansion of n, where g(n) = GCD of exponents e_k = A064894(n).

%I A064895 #14 Feb 13 2024 14:33:31
%S A064895 0,1,2,3,2,3,6,7,2,3,10,11,12,13,14,15,2,3,18,19,6,7,22,23,24,25,26,
%T A064895 27,28,29,30,31,2,3,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,
%U A064895 50,51,52,53,54,55,56,57,58,59,60,61,62,63,2,3,66,67,10,11,70,71,6,7,74,75
%N A064895 Binary concentration of n. Replace 2^e_k with 2^(e_k/g(n)) in binary expansion of n, where g(n) = GCD of exponents e_k = A064894(n).
%H A064895 Rémy Sigrist, <a href="/A064895/b064895.txt">Table of n, a(n) for n = 0..8192</a>
%F A064895 If n = 2^(g(n)e0) + 2^(g(n)e1) +... then a(n) = 2^e0 + 2^e1 +...
%e A064895 577 = 2^0 + 2^6 + 2^9, GCD(0,6,9) = 3, a(577) = 2^(0/3)+2^(6/3)+2^(9/3) = 13.
%t A064895 A064895[n_] := With[{e = Flatten[Position[Reverse[IntegerDigits[n, 2]], 1]] - 1}, Total[2^(e/Max[Apply[GCD, e], 1])]];
%t A064895 Array[A064895, 100, 0] (* _Paolo Xausa_, Feb 13 2024 *)
%o A064895 (PARI) a(n) = { my (b=vector(hammingweight(n))); for (i=1, #b, n-=2^b[i]=valuation(n,2);); b /= max(1, gcd(b)); sum(i=1, #b, 2^b[i]); } \\ _Rémy Sigrist_, Oct 16 2022
%Y A064895 Cf. A000079, A064894.
%K A064895 base,easy,nonn
%O A064895 0,3
%A A064895 _Marc LeBrun_, Oct 11 2001