The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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 (list; graph; refs; listen; history; text; internal format)
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
Sequence in context: A366901 A365551 A369015 * A334762 A358040 A305461
KEYWORD
nonn,easy,mult
AUTHOR
Amiram Eldar, Feb 15 2024
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 24 01:38 EDT 2024. Contains 372768 sequences. (Running on oeis4.)