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Search: id:A140826
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| A140826 |
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Arithmetic nondivisor means. |
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+0
2
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| 3, 4, 5, 7, 11, 13, 17, 18, 19, 20, 23, 24, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Numbers n such that a(n)=A024816(n)/(n-A000005(n)) is an integer.
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FORMULA
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Numbers n such that (n*n+n-2*sigma_1(n))/(2*n-2*sigma_0(n)) is an integer. sigma_1(n) the sum of divisors of n (A000203) sigma_0(n) the number of divisors of n (A000005)
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EXAMPLE
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n=18: numbers less than n which do not divide n are 4,5,7,8,10,11,12,13,14,15,16,17.
antisigma_1(18) = 4+5+7+8+10+11+12+13+14+15+16+17) = 132
sigma_0(18) = 12
132/12 = 11 which is an integer so n=18 belongs to the sequence.
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MAPLE
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A024816 := proc(n) n*(n+1)/2-numtheory[sigma](n) ; end: A000005 := proc(n) numtheory[tau](n) ; end: isA140826 := proc(n) if A024816(n) mod ( n-A000005(n)) = 0 then true; else false; fi; end: for n from 3 to 400 do if isA140826(n) then printf("%d, ", n) ; fi; od: [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Dec 13 2008]
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CROSSREFS
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Cf. A000005, A003601, A024816, A049820, A000203.
Sequence in context: A047499 A082378 A046642 this_sequence A081735 A107036 A001605
Adjacent sequences: A140823 A140824 A140825 this_sequence A140827 A140828 A140829
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KEYWORD
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easy,nonn
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AUTHOR
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Ctibor O. Zizka (ctibor.zizka(AT)seznam.cz), Jul 17 2008
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EXTENSIONS
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Inserted 20 and extended by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Dec 13 2008
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