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 A120737 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. 2
 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; text; internal format)
 OFFSET 1,2 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, 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). Numbers n for which tau(n)^phi(n) == 0 (mod n). [Paolo P. Lava, Jul 27 2012] LINKS Paolo P. Lava, Table of n, a(n) for n = 1..100 EXAMPLE d(32) = 6. 2 is the only prime dividing 32. 2 divides 6, so 32 is in the sequence. 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, Aug 17 2006 with(numtheory); A120737:=proc(q) local n; for n from 1 to q do if tau(n)^phi(n) mod n=0 then print(n); fi; od; end: A120737(10000); # Paolo P. Lava, Jul 27 2012. CROSSREFS Cf. A120736. Sequence in context: A033950 A046526 A057529 * A081381 A166686 A064833 Adjacent sequences:  A120734 A120735 A120736 * A120738 A120739 A120740 KEYWORD nonn AUTHOR Leroy Quet Jun 29 2006 EXTENSIONS More terms from R. J. Mathar, Aug 17 2006 STATUS approved

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