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!)
A324923 Number of distinct factors in the factorization of n into factors q(i) = prime(i)/i, i > 0. 33
0, 1, 2, 1, 3, 2, 2, 1, 2, 3, 4, 2, 3, 2, 3, 1, 3, 2, 2, 3, 3, 4, 3, 2, 3, 3, 2, 2, 4, 3, 5, 1, 4, 3, 4, 2, 3, 2, 3, 3, 4, 3, 3, 4, 3, 3, 4, 2, 2, 3, 4, 3, 2, 2, 4, 2, 3, 4, 4, 3, 3, 5, 3, 1, 4, 4, 3, 3, 3, 4, 4, 2, 4, 3, 3, 2, 5, 3, 5, 3, 2, 4, 4, 3, 5, 3, 4, 4, 3, 3, 4, 3, 5, 4, 4, 2, 4, 2, 4, 3, 4, 4, 3, 3, 4, 2, 3, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
COMMENTS
Also the number of distinct proper terminal subtrees of the rooted tree with Matula-Goebel number n. See illustrations in A061773.
LINKS
FORMULA
a(n) = A317713(n) - 1.
a(n) = A196050(n) - A366386(n). - Antti Karttunen, Oct 23 2023
EXAMPLE
The factorization 22 = q(1)^2 q(2) q(3) q(5) has four distinct factors, so a(22) = 4.
MATHEMATICA
difac[n_]:=If[n==1, {}, With[{i=PrimePi[FactorInteger[n][[1, 1]]]}, Sort[Prepend[difac[n*i/Prime[i]], i]]]];
Table[Length[Union[difac[n]]], {n, 100}]
PROG
(PARI)
A006530(n) = if(1==n, n, my(f=factor(n)); f[#f~, 1]);
A324923(n) = { my(lista = List([]), gpf, i); while(n > 1, gpf=A006530(n); i = primepi(gpf); n /= gpf; n *= i; listput(lista, i)); #Set(lista); }; \\ Antti Karttunen, Oct 23 2023
CROSSREFS
One less than A317713.
Sequence in context: A303639 A090000 A109082 * A126303 A306467 A157810
KEYWORD
nonn
AUTHOR
Gus Wiseman, Mar 20 2019
EXTENSIONS
Data section extended up to a(108) by Antti Karttunen, Oct 23 2023
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 March 29 05:16 EDT 2024. Contains 371264 sequences. (Running on oeis4.)