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 A144486 Triangular numbers n*(n+1)/2 with n and n+1 composite, where number of prime factors in n = number of prime factors in n+1. (Prime factors are counted with multiplicity.) 1
 45, 105, 231, 325, 378, 561, 595, 741, 990, 1653, 2850, 3655, 3741, 4371, 4465, 4851, 6786, 7021, 7381, 7503, 7750, 8911, 9180, 10011, 10153, 10585, 10878, 11781, 12561, 13530, 14535, 14706, 15225, 15753, 20301, 20503, 21115, 22791, 23005, 23653 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS FORMULA a(n) = A000217(A045920(n+1)). EXAMPLE The first 11 values of n that satisfy the definition are 9, 14, 21, 25, 27, 33, 34, 38, 44, 57 and 75, so a(1) = 9*10/2 = 45; 9 = 3*3, 10 = 2*5. a(2) = 14*15/2 = 105; 14 = 2*7, 14 = 3*5. a(3) = 21*22/2 = 231; 21 = 3*7, 22 = 2*11. a(4) = 25*26/2 = 325; 25 = 5*5, 26 = 2*13. a(5) = 27*28/2 = 378; 27 = 3*3*3, 28 = 2*2*7. a(6) = 33*34/2 = 561; 33 = 3*11, 34 = 2*17. a(7) = 34*35/2 = 595; 34 = 2*17, 35 = 5*7. a(8) = 38*39/2 = 741; 38=2*19, 39=3*13. a(9) = 44*45/2 = 990; 44=2*2*11, 45=3*3*5. a(10) = 57*58/2 = 1653; 57=3*19, 58=2*29. a(11) = 75*76/2 = 2850; 75=3*5*5, 76=2*2*19. MAPLE isA045920 := proc(n) if numtheory[bigomega](n) = numtheory[bigomega](n+1) then true; else false; fi; end: A045920 := proc(n) option remember ; local a; if n =1 then 2; else for a from procname(n-1)+1 do if isA045920(a) then RETURN(a) ; fi; od: fi; end: A000217 := proc(n) n*(n+1)/2 ; end: A144486 := proc(n) A000217(A045920(n+1)) ; end: for n from 1 to 100 do printf("%d, ", A144486(n)) ; od: # R. J. Mathar, Dec 10 2008 MATHEMATICA Times@@#/2&/@Select[Partition[Range[500], 2, 1], !PrimeQ[#[[1]]] && !PrimeQ #[[2]]] && PrimeOmega[#[[1]]]==PrimeOmega[#[[2]]]&] (* Harvey P. Dale, May 23 2013 *) PROG (PARI) for(n=2, 1e3, if(bigomega(n+1) == bigomega(n+2) && k = (n+1)*(n+2)/2, print1(k", "))) \\ Altug Alkan, Oct 18 2015 CROSSREFS Cf. A144291. Sequence in context: A068355 A331190 A332593 * A199351 A199517 A180971 Adjacent sequences:  A144483 A144484 A144485 * A144487 A144488 A144489 KEYWORD nonn,easy AUTHOR Juri-Stepan Gerasimov, Dec 09 2008 EXTENSIONS Corrected and extended by R. J. Mathar and Ray Chandler, Dec 10 2008 STATUS approved

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Last modified June 24 11:45 EDT 2021. Contains 345416 sequences. (Running on oeis4.)