cp's OEIS Frontend

A331736 The largest odd divisor of A225546(n).

%I A331736 #14 Feb 15 2020 08:04:20
%S A331736 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,
%T A331736 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,
%U A331736 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
%N A331736 The largest odd divisor of A225546(n).
%H A331736 Antti Karttunen, <a href="/A331736/b331736.txt">Table of n, a(n) for n = 1..1680</a>
%F A331736 Multiplicative, with a(prime(i)^j) = A000265(A019565(j))^A000079(i-1).
%F A331736 Equally, with a(prime(i)^j) = A019565(A052928(j))^A000079(i-1).
%F A331736 a(n) = A000265(A225546(n)).
%F A331736 a(n) = A225546(A008833(n)).
%t A331736 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 *)
%o A331736 (PARI)
%o A331736 A019565(n) = factorback(vecextract(primes(logint(n+!n, 2)+1), n));
%o A331736 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); };
%o A331736 (PARI)
%o A331736 A048675(n) = { my(f = factor(n)); sum(k=1, #f~, f[k, 2]*2^primepi(f[k, 1]))/2; };
%o A331736 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])));
%Y A331736 Cf. A000265, A005117, A008833, A052928, A225546.
%K A331736 nonn,mult
%O A331736 1,4
%A A331736 _Antti Karttunen_, Feb 02 2020