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A120737
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A number n is included if it satisfies: the prime p divides d(n) for all p's where p divides n, d(n) = number of positive divisors of n.
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1
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1, 2, 8, 9, 12, 18, 32, 72, 80, 96, 108, 128, 243, 288, 448, 486, 512, 625, 720, 768, 864, 972, 1152, 1200, 1250, 1620, 1944, 2000, 2025, 2048, 2560, 2592, 3888, 4032, 4050, 4608, 5000, 5625, 6144, 6561, 6912, 7500, 7776, 8192, 8748, 9408, 10800, 11250
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Numbers n such that A000005(n)/A007947(n) is an integer. The sequence A070226 is a subsequence of this sequence. Conjecture : If A000005(n) divides A007947(n) for some n, then A007947(n)/A000005(n)=1. [From Ctibor O. Zizka (c.zizka(AT)email.cz), Feb 05 2009]
Contribution from Leroy Quet, May 23 2009: (Start)
This sequence contains exactly those positive integers n where 1 is the only positive divisor of n that is coprime to d(n).
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EXAMPLE
| d(32) = 6. 2 is the only prime dividing 32. 2 divides 6, so 32 is in the sequence.
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MAPLE
| isA120737 := proc(n) local d, p; d := numtheory[tau](n) ; p := 2 ; while p <= n do if ( n mod p ) = 0 then if ( d mod p ) <> 0 then RETURN(false) ; fi ; fi ; p := nextprime(p) ; od ; RETURN(true) ; end: for n from 1 to 12000 do if isA120737(n) then printf("%d, ", n) ; fi ; od ; - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Aug 17 2006
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CROSSREFS
| Cf. A120736.
Sequence in context: A033950 A046526 A057529 * A081381 A166686 A064833
Adjacent sequences: A120734 A120735 A120736 * A120738 A120739 A120740
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KEYWORD
| nonn
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AUTHOR
| Leroy Quet Jun 29 2006
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EXTENSIONS
| More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Aug 17 2006
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