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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A008481 If n = Product (p_j^k_j) then a(n) = Sum partition(k_j). 4
0, 1, 1, 2, 1, 2, 1, 3, 2, 2, 1, 3, 1, 2, 2, 5, 1, 3, 1, 3, 2, 2, 1, 4, 2, 2, 3, 3, 1, 3, 1, 7, 2, 2, 2, 4, 1, 2, 2, 4, 1, 3, 1, 3, 3, 2, 1, 6, 2, 3, 2, 3, 1, 4, 2, 4, 2, 2, 1, 4, 1, 2, 3, 11, 2, 3, 1, 3, 2, 3, 1, 5, 1, 2, 3, 3, 2, 3, 1, 6, 5, 2, 1, 4, 2, 2, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

a(n) is a function of the prime signature of n (cf. A025487). - Matthew Vandermast, Jun 24 2012

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..65537 (first 10000 terms from Vincenzo Librandi)

Index entries for sequences computed from exponents in factorization of n

FORMULA

Additive with a(p^e) = A000041(e); a(n) = A007814(A318312(n)). - Antti Karttunen, Aug 30 2018

MAPLE

a:= n-> add(combinat[numbpart](i[2]), i=ifactors(n)[2]):

seq(a(n), n=1..100);  # Alois P. Heinz, Aug 30 2018

MATHEMATICA

Prepend[ Array[ Plus @@ (PartitionsP /@ Last[ Transpose[ FactorInteger[ # ] ] ])&, 100, 2 ], 0 ]

(* Second program: *)

Array[Total[PartitionsP /@ FactorInteger[#][[All, -1]] - Boole[# == 1]] &, 87] (* Michael De Vlieger, Sep 02 2018 *)

PROG

(PARI) A008481(n) = vecsum(apply(e -> numbpart(e), factor(n)[, 2])); \\ Antti Karttunen, Aug 30 2018

CROSSREFS

Cf. A000041, A318312.

Differs from A318473 for the first time at n=32, where a(32)=7, while A318473(32)=8.

Sequence in context: A098893 A302037 A069248 * A318473 A127669 A323436

Adjacent sequences:  A008478 A008479 A008480 * A008482 A008483 A008484

KEYWORD

nonn

AUTHOR

Olivier Gérard

EXTENSIONS

Term a(1) corrected from 1 to 0 (for an empty sum) by Antti Karttunen, Aug 30 2018

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 March 21 01:18 EDT 2019. Contains 321356 sequences. (Running on oeis4.)