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 A120736 Numbers n such that every prime p that divides d(n) (A000005) also divides n. 11
 1, 2, 6, 8, 9, 10, 12, 14, 18, 22, 24, 26, 30, 34, 36, 38, 40, 42, 46, 54, 56, 58, 60, 62, 66, 70, 72, 74, 78, 80, 82, 84, 86, 88, 90, 94, 96, 102, 104, 106, 108, 110, 114, 118, 120, 122, 126, 128, 130, 132, 134, 136, 138, 142, 146, 150, 152, 154, 156, 158, 166, 168 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Numbers n for which n^phi(n) == 0 (mod tau(n)). - Paolo P. Lava, Jul 27 2012 Sequence is identical to A048751 except for terms 1 and 2 that are included here. - Michel Marcus, Jun 06 2014 Numbers n such that tau(n) = A000005(n) divides product of the divisors of n (A007955). - Jaroslav Krizek, Sep 05 2017 LINKS Paolo P. Lava, Table of n, a(n) for n = 1..10000 EXAMPLE d(26) = 4. 2 is the only prime dividing 4. 2 divides 26, so 26 is in the sequence. MAPLE isA120736 := proc(n) local d, p; d := numtheory[tau](n) ; p := 2 ; while p <= n do if ( d mod p ) = 0 then if ( n mod p ) <> 0 then RETURN(false) ; fi ; fi ; p := nextprime(p) ; od ; RETURN(true) ; end: for n from 1 to 200 do if isA120736(n) then printf("%d, ", n) ; fi ; od ; # R. J. Mathar, Aug 17 2006 with(numtheory); A120736:=proc(q) local n; for n from 1 to q do if n^phi(n) mod tau(n)=0 then print(n); fi; od; end: A120736(10000); # Paolo P. Lava, Jul 27 2012 MATHEMATICA Select[Range@ 168, Divisible[Times @@ Divisors@ #, DivisorSigma[0, #]] &] (* Michael De Vlieger, Sep 05 2017 *) PROG (Magma) [n: n in [1..1000] | Denominator(&*[d: d in Divisors(n)] / #[d: d in Divisors(n)]) eq 1]; // Jaroslav Krizek, Sep 05 2017 CROSSREFS Cf. A000005, A120737. Sequence in context: A077477 A095879 A342751 * A130099 A047397 A174331 Adjacent sequences: A120733 A120734 A120735 * A120737 A120738 A120739 KEYWORD nonn AUTHOR Leroy Quet, Jun 29 2006 EXTENSIONS More terms from R. J. Mathar, Aug 17 2006 STATUS approved

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Last modified March 25 19:21 EDT 2023. Contains 361528 sequences. (Running on oeis4.)