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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).
2
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, 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, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1
OFFSET
1,8
COMMENTS
First differs from A270419 at n = 128.
LINKS
FORMULA
Multiplicative with a(p^e) = p^(2^ceiling(log_2(e)) - e).
a(n) = A356194(n)/n.
a(n) = 1 if and only if n is in A138302.
MATHEMATICA
f[p_, e_] := p^(2^Ceiling[Log2[e]] - e); a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100]
PROG
(PARI) s(n) = {my(e = logint(n, 2)); if(n == 2^e, 0, 2^(e+1) - n)};
a(n) = {my(f = factor(n)); prod(i = 1, #f~, f[i, 1]^s(f[i, 2]))};
CROSSREFS
KEYWORD
nonn,easy,mult
AUTHOR
Amiram Eldar, Aug 31 2023
STATUS
approved