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!)
A264857 Number of values of k, n included, such that the distinct prime divisors of k are the same as those of n and Omega(k) = Omega(n), where Omega(n) is the number of prime divisors of n with multiplicity (A001222); a(1) = 1. 1
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 3, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 3, 1, 1, 1, 2, 2, 1, 1, 4, 1, 2, 1, 2, 1, 3, 1, 3, 1, 1, 1, 3, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 4, 1, 1, 2, 2, 1, 1, 1, 4, 1, 1, 1, 3, 1, 1, 1, 3, 1, 3, 1, 2, 1, 1, 1, 5, 1, 2, 2, 3 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,12
COMMENTS
a(n) > 1 if 1 < omega(n) < Omega(n), where omega(n) is the number of distinct prime divisors of n (A001221).
a(n) = 1 if n is a squarefree number (A005117) or a prime power p^e where p is a prime and e >= 2 (A246547).
LINKS
FORMULA
a(n) = C(A001222(n)-1, A001221(n)-1). - Robert Israel, Nov 27 2015
EXAMPLE
The numbers k with the same prime divisors 2 and 3 are (6, 12, 18, 24, 30, 36, 42, 48, 54, 60, ...) and those for which A001222(k) = 3 are (12, 18), so a(12) = a(18) = 2.
The numbers k with the same prime divisor 5 are (5, 25, 125, 625, 3125, ...) and those for which A001222(k) = 4 are (625), so a(625) = 1.
MAPLE
seq(binomial(numtheory:-bigomega(n)-1, nops(numtheory:-factorset(n))-1) , n=1..200); # Robert Israel, Nov 27 2015
MATHEMATICA
Table[Binomial[PrimeOmega@ n - 1, PrimeNu@ n - 1], {n, 100}] (* Michael De Vlieger, Nov 28 2015 *)
PROG
(PARI) a(n) = if(n==1, 1, binomial(bigomega(n)-1, omega(n)-1)) \\ Altug Alkan, Dec 04 2015
CROSSREFS
Sequence in context: A030612 A371921 A327528 * A370645 A340596 A340654
KEYWORD
nonn
AUTHOR
Gionata Neri, Nov 26 2015
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 June 16 23:34 EDT 2024. Contains 373432 sequences. (Running on oeis4.)