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Search: id:A145739
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| A145739 |
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Numbers n for which the sum of all divisors of n <= sqrt(n) is a divisor of n. |
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+0
1
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| 1, 2, 3, 5, 6, 7, 11, 12, 13, 17, 18, 19, 23, 28, 29, 31, 37, 41, 43, 45, 47, 48, 53, 56, 59, 61, 67, 71, 72, 73, 79, 80, 83, 89, 96, 97, 101, 103, 107, 109, 113, 117, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 196, 197, 199, 211, 223, 227
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Includes all prime numbers. Includes all even perfect numbers. Includes no power of 2 > 2. Includes no number of the form 2p where p is a prime number greater than 3
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FORMULA
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{n: A066839(n) | n}. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 02 2008]
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EXAMPLE
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4 does not qualify for this sequence because the divisors of 4 <= sqrt(4) are 1 and 2 and 1+2=3 and 3 is not a divisor of 4.
12 is in the sequence because the divisors of 12 <= sqrt(12) are 1, 2 and 3 and 1+2+3=6 is a divisor of 12. [From Emeric Deutsch (deutsch(AT)duke.poly.edu), Oct 27 2008]
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MAPLE
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with(numtheory): a:=proc(n) local div, s, j: div:=divisors(n): s:=0: for j while div[j] <= evalf(sqrt(n)) do s:=s+div[j] end do: if type(n/s, integer) = true then n else end if end proc: 1, seq(a(n), n=2..250); [From Emeric Deutsch (deutsch(AT)duke.poly.edu), Oct 27 2008]
A066839 := proc(n) local a, d ; a := 0 ; for d in numtheory[divisors](n) do if d^2 <= n then a := a+d ; fi; od: a ; end: A145739 := proc(n) option remember ; local a; if n = 1 then 1; else for a from procname(n-1)+1 do if a mod A066839(a) = 0 then RETURN(a) ; fi; od: fi; end: for n from 1 to 300 do printf("%d, ", A145739(n)) ; od: [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 02 2008]
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CROSSREFS
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Sequence in context: A059041 A129128 A164922 this_sequence A121700 A080980 A134669
Adjacent sequences: A145736 A145737 A145738 this_sequence A145740 A145741 A145742
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KEYWORD
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nonn
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AUTHOR
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J. Lowell (jhbubby(AT)mindspring.com), Oct 17 2008
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EXTENSIONS
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More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl) and Emeric Deutsch (deutsch(AT)duke.poly.edu), Nov 01 2008
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