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A064895
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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).
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4
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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, 27, 28, 29, 30, 31, 2, 3, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 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
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OFFSET
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0,3
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LINKS
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FORMULA
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If n = 2^(g(n)e0) + 2^(g(n)e1) +... then a(n) = 2^e0 + 2^e1 +...
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EXAMPLE
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577 = 2^0 + 2^6 + 2^9, GCD(0,6,9) = 3, a(577) = 2^(0/3)+2^(6/3)+2^(9/3) = 13.
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MATHEMATICA
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A064895[n_] := With[{e = Flatten[Position[Reverse[IntegerDigits[n, 2]], 1]] - 1}, Total[2^(e/Max[Apply[GCD, e], 1])]];
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PROG
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(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
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CROSSREFS
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KEYWORD
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base,easy,nonn
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AUTHOR
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STATUS
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approved
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