

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
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OFFSET

1,1


LINKS

Table of n, a(n) for n=1..47.


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[110], !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[2]: f in Factorization(k) ] + &+[ f[2]: 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

JuriStepan 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



