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A331736
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The largest odd divisor of A225546(n).
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3
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1, 1, 1, 3, 1, 1, 1, 3, 9, 1, 1, 3, 1, 1, 1, 5, 1, 9, 1, 3, 1, 1, 1, 3, 81, 1, 9, 3, 1, 1, 1, 5, 1, 1, 1, 27, 1, 1, 1, 3, 1, 1, 1, 3, 9, 1, 1, 5, 6561, 81, 1, 3, 1, 9, 1, 3, 1, 1, 1, 3, 1, 1, 9, 15, 1, 1, 1, 3, 1, 1, 1, 27, 1, 1, 81, 3, 1, 1, 1, 5, 25, 1, 1, 3, 1, 1, 1, 3, 1, 9, 1, 3, 1, 1, 1, 5, 1, 6561, 9, 243, 1, 1, 1, 3, 1
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OFFSET
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1,4
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LINKS
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FORMULA
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MATHEMATICA
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Array[#/2^IntegerExponent[#, 2] &@ If[# == 1, 1, Times @@ Flatten@ Map[Function[{p, e}, Map[Prime[Log2@ # + 1]^(2^(PrimePi@ p - 1)) &, DeleteCases[NumberExpand[e, 2], 0]]] @@ # &, FactorInteger[#]]] &, 105] (* Michael De Vlieger, Feb 12 2020 *)
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PROG
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(PARI)
A019565(n) = factorback(vecextract(primes(logint(n+!n, 2)+1), n));
A331736(n) = { my(f=factor(n)); for (i=1, #f~, my(p=f[i, 1]); f[i, 1] = A019565((f[i, 2]>>1)<<1); f[i, 2] = 2^(primepi(p)-1); ); factorback(f); };
(PARI)
A048675(n) = { my(f = factor(n)); sum(k=1, #f~, f[k, 2]*2^primepi(f[k, 1]))/2; };
A331736(n) = if(1==n, 1, my(f=factor(n), u=#binary(vecmax(f[, 2])), prods=vector(u, x, 1), m=2, e); for(i=2, u, for(k=1, #f~, if(bitand(f[k, 2], m), prods[i] *= f[k, 1])); m<<=1); prod(i=2, u, prime(i)^A048675(prods[i])));
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CROSSREFS
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KEYWORD
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nonn,mult
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AUTHOR
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STATUS
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approved
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