login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A143201 Product of distances between prime factors in factorization of n. 16
1, 1, 1, 1, 1, 2, 1, 1, 1, 4, 1, 2, 1, 6, 3, 1, 1, 2, 1, 4, 5, 10, 1, 2, 1, 12, 1, 6, 1, 6, 1, 1, 9, 16, 3, 2, 1, 18, 11, 4, 1, 10, 1, 10, 3, 22, 1, 2, 1, 4, 15, 12, 1, 2, 7, 6, 17, 28, 1, 6, 1, 30, 5, 1, 9, 18, 1, 16, 21, 12, 1, 2, 1, 36, 3, 18, 5, 22, 1, 4, 1, 40, 1, 10, 13, 42, 27, 10, 1, 6, 7, 22 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,6

COMMENTS

a(A007947(n)) = a(n);

A006093 and A001747 give record values and where they occur:

A006093(n)=a(A001747(n+1)) for n>1.

a(n) = 1 iff n is a prime power: a(A000961(n))=1;

a(n) = 2 iff n has exactly 2 and 3 as prime factors:

a(A033845(n))=2;

a(n) = 3 iff n is in A143202;

a(n) = 4 iff n has exactly 2 and 5 as prime factors:

a(A033846(n))=4;

a(n) = 5 iff n is in A143203;

a(n) = 6 iff n is in A143204;

a(n) = 7 iff n is in A143205;

a(n) <> A006512(k)+1 for k>1.

a(A033849(n))=3; a(A033851(n))=3; a(A033850(n))=5; a(A033847(n))=6; a(A033848(n))=10. [Reinhard Zumkeller, Sep 19 2011]

LINKS

R. Zumkeller, Table of n, a(n) for n = 1..10000

Index entries for primes, gaps between

FORMULA

a(n) = f(n,1,1) where f(n,q,y) = if n=1 then y else if q=1 then f(n/p,p,1)) else f(n/p,p,y*(p-q+1)) with p = A020639(n) = smallest prime factor of n.

EXAMPLE

a(86) = a(43*2) = 43-2+1 = 42;

a(138) = a(23*3*2) = (23-3+1)*(3-2+1) = 42;

a(172) = a(43*2*2) = (43-2+1)*(2-2+1) = 42;

a(182) = a(13*7*2) = (13-7+1)*(7-2+1) = 42;

a(276) = a(23*3*2*2) = (23-3+1)*(3-2+1)*(2-2+1) = 42;

a(330) = a(11*5*3*2) = (11-5+1)*(5-3+1)*(3-2+1) = 42.

MATHEMATICA

Table[Times@@(Differences[Flatten[Table[First[#], {Last[#]}]&/@ FactorInteger[ n]]]+1), {n, 100}] (* Harvey P. Dale, Dec 07 2011 *)

PROG

(Haskell)

a143201 1 = 1

a143201 n = product $ map (+ 1) $ zipWith (-) (tail pfs) pfs

   where pfs = a027748_row n

-- Reinhard Zumkeller, Sep 13 2011

CROSSREFS

Cf. A109313.

Cf. A027748.

Sequence in context: A174204 A118106 A324574 * A254048 A306671 A308210

Adjacent sequences:  A143198 A143199 A143200 * A143202 A143203 A143204

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, Aug 12 2008

STATUS

approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 17 05:27 EST 2019. Contains 329217 sequences. (Running on oeis4.)