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Search: id:A120350
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| A120350 |
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Refactorable numbers such that the number of odd divisors r and the number of even divisors s are both divisors of n. |
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+0
1
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| 2, 12, 18, 24, 36, 72, 80, 180, 240, 252, 360, 396, 450, 468, 480, 504, 560, 612, 684, 720, 792, 828, 880, 882, 896, 936, 972, 1040, 1044, 1116, 1200, 1224, 1250, 1332, 1344, 1360, 1368, 1440, 1476, 1520, 1548, 1620, 1656, 1692, 1840, 1908, 1944, 2000
(list; graph; listen)
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OFFSET
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0,1
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COMMENT
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Since s=0 if n is odd, the number n is necessarily even and then s is always a multiple of r. Note that t=r+s may not be a divisor even if both r and s are divisors. For example, if n=144, then r=3, s=12, but t=r+s=15.
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FORMULA
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a(n) = n is even, r = number of odd divisors of n, s = number of even divisors of n and t = r + s = number of divisors of n, are all divisors of n.
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EXAMPLE
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a(3)=18 since r=3, s=3 and t=r+s=6 are all divisors.
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MAPLE
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with(numtheory); A:=[]: for w to 1 do for k from 1 to 5000 do n:=2*k; S:=divisors(n); r:=nops( select(z->type(z, odd), S) ); s:=nops( select(z->type(z, even), S) ); t:=r+s; if andmap(z -> n mod z = 0, [r, s, t]) then A:=[op(A), n]; print(n, r, s, t); fi; od od; A;
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CROSSREFS
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Cf. A033950, A049439, A057265.
Sequence in context: A082407 A063576 A144264 this_sequence A032413 A066238 A101074
Adjacent sequences: A120347 A120348 A120349 this_sequence A120351 A120352 A120353
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KEYWORD
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nonn
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AUTHOR
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Walter Kehowski (wkehowski(AT)cox.net), Jun 24 2006
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