A369890 The number of divisors of the largest divisor of n whose exponents in its prime factorization are all powers of 2.

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

Amiram Eldar, Table of n, a(n) for n = 1..10000

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

Cf. A000005, A000079, A053644, A138302, A353897, A369015.

Sequence in context: A366901 A365551 A369015 * A334762 A358040 A305461

Adjacent sequences: A369887 A369888 A369889 * A369891 A369892 A369893

Keyword

nonn,easy,mult

Author

Amiram Eldar, Feb 15 2024

Status

approved