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A120737
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Numbers k whose number of divisors d(k) is divisible by every prime factor of k.
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6
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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
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OFFSET
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1,2
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COMMENTS
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This sequence contains exactly those positive integers k where 1 is the only positive divisor of k that is coprime to d(k). - Leroy Quet, May 23 2009
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LINKS
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EXAMPLE
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d(32) = 6. 2 is the only prime dividing 32. 2 divides 6, so 32 is in the sequence.
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MAPLE
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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 ;
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MATHEMATICA
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divQ[n_] := AllTrue[FactorInteger[n][[;; , 1]], Divisible[DivisorSigma[0, n], #] &]; Select[Range[10^4], divQ] (* Amiram Eldar, Nov 08 2020 *)
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PROG
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(PARI) isok(k) = Mod(numdiv(k), k)^eulerphi(k) == 0; \\ Michel Marcus, May 11 2019
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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