cp's OEIS Frontend

A365297 a(n) is the smallest number k such that k*n is a number whose prime factorization exponents are all powers of 2 (A138302).

%I A365297 #7 Aug 31 2023 12:17:06
%S A365297 1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,1,3,1,1,1,1,8,1,1,
%T A365297 1,1,1,1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,3,1,2,1,1,1,1,1,1,1,4,1,1,1,1,
%U A365297 1,1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1
%N A365297 a(n) is the smallest number k such that k*n is a number whose prime factorization exponents are all powers of 2 (A138302).
%C A365297 First differs from A270419 at n = 128.
%H A365297 Amiram Eldar, <a href="/A365297/b365297.txt">Table of n, a(n) for n = 1..10000</a>
%F A365297 Multiplicative with a(p^e) = p^(2^ceiling(log_2(e)) - e).
%F A365297 a(n) = A356194(n)/n.
%F A365297 a(n) = 1 if and only if n is in A138302.
%t A365297 f[p_, e_] := p^(2^Ceiling[Log2[e]] - e); a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100]
%o A365297 (PARI) s(n) = {my(e = logint(n, 2)); if(n == 2^e, 0, 2^(e+1) - n)};
%o A365297 a(n) = {my(f = factor(n)); prod(i = 1, #f~, f[i, 1]^s(f[i, 2]))};
%Y A365297 Cf. A138302, A270419, A356194.
%K A365297 nonn,easy,mult
%O A365297 1,8
%A A365297 _Amiram Eldar_, Aug 31 2023