The OEIS is supported by the many generous donors to the OEIS Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A144581 Triangular numbers k*(k+1)/2 such that (number of prime factors of k) + (number of prime factors of k+1) is composite. 1
 28, 45, 66, 78, 105, 120, 153, 171, 190, 231, 300, 325, 378, 406, 435, 465, 496, 561, 595, 630, 741, 780, 861, 903, 946, 990, 1128, 1378, 1485, 1540, 1596, 1653, 2016, 2080, 2211, 2278, 2485, 2556, 2628, 2850, 3081, 3160, 3240, 3321, 3570, 3655, 3741 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS EXAMPLE 7 has one prime factor and 8 = 2*2*2 has three prime factors; 1+3 = 4 is composite, hence 7*8/2 = 28 is in the sequence. 15 = 3*5 has two prime factors and 16=2*2*2*2 has four prime factors; 2+4 = 6 is composite, hence 15*16/2 = 120 is in the sequence. 18 = 2*3*3 has three prime factors and 19 has one prime factors; 3+1 = 4 is composite, hence 18*19/2 = 171 is in the sequence. MATHEMATICA (#(#+1))/2&/@Rest[Select[Range, !PrimeQ[PrimeOmega[#] + PrimeOmega[ #+1]]&]] (* Harvey P. Dale, Mar 18 2012 *) PROG (Magma) [ k*(k+1)/2: k in [2..86] | not IsPrime(s) where s is &+[ f: f in Factorization(k) ] + &+[ f: f in Factorization(k+1) ] ]; CROSSREFS Cf. A000217 (triangular numbers), A002808 (composite numbers). See A144552 for another version. Sequence in context: A169962 A219685 A180045 * A075875 A332764 A116541 Adjacent sequences: A144578 A144579 A144580 * A144582 A144583 A144584 KEYWORD nonn AUTHOR Juri-Stepan Gerasimov, Dec 31 2008 EXTENSIONS Edited and corrected by Klaus Brockhaus, Jan 03 2009 Edited by N. J. A. Sloane, Jan 08 2009 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.

Last modified April 1 19:13 EDT 2023. Contains 361695 sequences. (Running on oeis4.)