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A369890
The number of divisors of the largest divisor of n whose exponents in its prime factorization are all powers of 2.
1
1, 2, 2, 3, 2, 4, 2, 3, 3, 4, 2, 6, 2, 4, 4, 5, 2, 6, 2, 6, 4, 4, 2, 6, 3, 4, 3, 6, 2, 8, 2, 5, 4, 4, 4, 9, 2, 4, 4, 6, 2, 8, 2, 6, 6, 4, 2, 10, 3, 6, 4, 6, 2, 6, 4, 6, 4, 4, 2, 12, 2, 4, 6, 5, 4, 8, 2, 6, 4, 8, 2, 9, 2, 4, 6, 6, 4, 8, 2, 10, 5, 4, 2, 12, 4, 4
OFFSET
1,2
COMMENTS
First differs from A369015 at n = 32.
LINKS
FORMULA
a(n) = A000005(A353897(n)).
Multiplicative with a(p^e) = A053644(e) + 1.
a(n) = 2 if and only if n is prime.
a(n) <= A000005(n), with equality if and only if n is in A138302.
MATHEMATICA
f[p_, e_] := 2^Floor[Log2[e]] + 1; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100]
PROG
(PARI) a(n) = vecprod(apply(x -> 2^logint(x, 2) + 1, factor(n)[, 2]));
CROSSREFS
KEYWORD
nonn,easy,mult
AUTHOR
Amiram Eldar, Feb 15 2024
STATUS
approved