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Search: id:A137428
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| A137428 |
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Positive integers n such that the largest prime divisor of n is > at least one composite divisor of n. |
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+0
1
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| 20, 28, 40, 42, 44, 52, 56, 60, 66, 68, 76, 78, 80, 84, 88, 92, 99, 100, 102, 104, 110, 112, 114, 116, 117, 120, 124, 126, 130, 132, 136, 138, 140, 148, 152, 153, 156, 160, 164, 168, 170, 171, 172, 174, 176, 180, 184, 186, 188, 190, 196, 198, 200, 204, 207, 208
(list; graph; listen)
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OFFSET
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1,1
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EXAMPLE
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The positive divisors of 60 are 1,2,3,4,5,6,10,12,15,20,30,60. The divisor 4, a composite, is less than the prime divisor 5. So 60 is in this sequence.
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MAPLE
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isA137428 := proc(n) local dvs, p, i ; dvs := sort(convert(numtheory[divisors](n) minus{1}, list)) ; for i from 1 to nops(dvs) do if isprime(op(-i, dvs)) then p := op(-i, dvs) ; break ; fi ; od: for i from 1 to nops(dvs) do if op(i, dvs) < p and not isprime(op(i, dvs)) then RETURN(true) ; fi ; od: RETURN(false) ; end: for n from 1 to 400 do if isA137428(n) then printf("%d, ", n) ; fi ; od: - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 21 2008
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MATHEMATICA
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a = {}; For[n = 2, n < 300, n++, If[FactorInteger[n][[ -1, 1]] > Min[Select[ Divisors[n], ! PrimeQ[ # ]&& # > 1 &]], AppendTo[a, n]]]; a - Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Apr 21 2008
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CROSSREFS
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Cf. A006530, A088739.
Sequence in context: A024411 A139805 A141823 this_sequence A124318 A139703 A145567
Adjacent sequences: A137425 A137426 A137427 this_sequence A137429 A137430 A137431
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KEYWORD
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nonn
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AUTHOR
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Leroy Quet (q1qq2qqq3qqqq(AT)yahoo.com), Apr 17 2008
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EXTENSIONS
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More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl) and Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Apr 21 2008
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