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A369760
The number of divisors of the smallest multiple of n whose prime factorization exponents are all powers of 2.
3
1, 2, 2, 3, 2, 4, 2, 5, 3, 4, 2, 6, 2, 4, 4, 5, 2, 6, 2, 6, 4, 4, 2, 10, 3, 4, 5, 6, 2, 8, 2, 9, 4, 4, 4, 9, 2, 4, 4, 10, 2, 8, 2, 6, 6, 4, 2, 10, 3, 6, 4, 6, 2, 10, 4, 10, 4, 4, 2, 12, 2, 4, 6, 9, 4, 8, 2, 6, 4, 8, 2, 15, 2, 4, 6, 6, 4, 8, 2, 10, 5, 4, 2, 12
OFFSET
1,2
LINKS
FORMULA
a(n) = A000005(A356194(n)).
Multiplicative with a(p^e) = 2^ceiling(log_2(e)) + 1.
a(n) >= A000005(n), with equality if and only if n is in A138302.
MATHEMATICA
f[p_, e_] := 2^Ceiling[Log2[e]] + 1; 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, n, 2^(e+1))};
a(n) = vecprod(apply(x -> s(x) + 1, factor(n)[, 2]));
CROSSREFS
KEYWORD
nonn,easy,mult
AUTHOR
Amiram Eldar, Jan 31 2024
STATUS
approved