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!)
A069904 Number of prime factors of n-th triangular number (with multiplicity). 13
0, 1, 2, 2, 2, 2, 3, 4, 3, 2, 3, 3, 2, 3, 5, 4, 3, 3, 3, 4, 3, 2, 4, 5, 3, 4, 5, 3, 3, 3, 5, 6, 3, 3, 5, 4, 2, 3, 5, 4, 3, 3, 3, 5, 4, 2, 5, 6, 4, 4, 4, 3, 4, 5, 5, 5, 3, 2, 4, 4, 2, 4, 8, 7, 4, 3, 3, 4, 4, 3, 5, 5, 2, 4, 5, 4, 4, 3, 5, 8, 5, 2, 4, 5, 3, 3, 5, 4, 4, 5 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
LINKS
FORMULA
a(n) = A001222(A000217(n)).
From Antti Karttunen, Oct 07 2017: (Start)
a(n) = (A001222(n)+A001222(n+1))-1.
a(n) = A001222(A278253(n)). (End)
From Alois P. Heinz, Aug 05 2019: (Start)
a(n) = 2 <=> n in { A164977 }.
a(n) = 3 <=> n in { A108815 }.
a(n) = 4 <=> n in { A114435 }.
a(n) = 5 <=> n in { A114436 }.
a(n) = 6 <=> n in { A114437 }.
a(n) = 7 <=> n in { A240527 }.
a(n) = 8 <=> n in { A240528 }.
a(n) = 9 <=> n in { A240529 }.
a(n) = 10 <=> n im { A101745 }. (End)
EXAMPLE
A000217(8) = 8*(8+1)/2 = 36 = 2*2*3*3, therefore a(8) = 4.
MATHEMATICA
Array[Plus@@Last/@FactorInteger[ #*(#+1)/2]&, 33] (* Vladimir Joseph Stephan Orlovsky, Feb 28 2010 *)
PROG
(PARI) A069904(n) = bigomega((n*(n+1))/2); \\ Antti Karttunen, Oct 07 2017
CROSSREFS
Sequence in context: A221530 A262944 A322789 * A164978 A119789 A025424
KEYWORD
nonn
AUTHOR
Reinhard Zumkeller, Apr 10 2002
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 19 04:26 EDT 2024. Contains 370952 sequences. (Running on oeis4.)