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Search: id:A144486
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| A144486 |
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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. |
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+0
1
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| 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; listen)
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OFFSET
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1,1
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FORMULA
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a(n) = A000217(A045920(n+1)).
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EXAMPLE
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If n=9=3*3 and n+1=10=2*5, then a(1)=45.
If n=14=2*7 and n+1=15=3*5, then a(2)=105.
If n=21=3*7 and n+1=22=2*11, then a(3)=231.
If n=25=5*5 and n+1=26=2*13, then a(4)=325.
If n=27=3*3*3 and n+1=28=2*2*7, then a(5)=378.
If n=33=3*11 and n+1=34=2*17, then a(6)=561.
If n=34=2*17 and n+1=35=5*7, then a(7)=595.
If n=38=2*19 and n+1=39=3*13, then a(8)=741.
If n=44=2*2*11 and n+1=45=3*3*5, then a(9)=990.
If n=57=3*19 and n+1=58=2*29, then a(10)=1653.
If n=75=3*5*5 and n+1=76=2*2*19, then a(11)=2850, etc.
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MAPLE
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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: [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Dec 10 2008]
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CROSSREFS
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Cf. A144291.
Sequence in context: A067828 A144552 A068355 this_sequence A043442 A044232 A044613
Adjacent sequences: A144483 A144484 A144485 this_sequence A144487 A144488 A144489
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KEYWORD
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nonn,easy
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AUTHOR
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Juri-Stepan Gerasimov (2stepan(AT)rambler.ru), Dec 09 2008
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EXTENSIONS
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Corrected and extended by R. J. Mathar (mathar(AT)strw.leidenuniv.nl) and Ray Chandler (rayjchandler(AT)sbcglobal.net), Dec 10 2008
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