A120736 Numbers k such that every prime p that divides d(k) (A000005) also divides k.

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

Offset: 1

Author

Leroy Quet, Jun 29 2006

Keywords

• nonn

Comments

Sequence is identical to A048751 except for terms 1 and 2 that are included here. - Michel Marcus, Jun 06 2014

Numbers k such that tau(k) = A000005(k) divides the product of the divisors of k (A007955). - Jaroslav Krizek, Sep 05 2017

Examples

			d(26) = 4. 2 is the only prime dividing 4. 2 divides 26, so 26 is in the sequence.
		

Links

• Paolo P. Lava, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000005, A120737.

Programs

Magma

[n: n in [1..1000] | Denominator(&*[d: d in Divisors(n)] / #[d: d in Divisors(n)]) eq 1];  // Jaroslav Krizek, Sep 05 2017

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

Mathematica

Select[Range@ 168, Divisible[Times @@ Divisors@ #, DivisorSigma[0, #]] &] (* Michael De Vlieger, Sep 05 2017 *)

Extensions

More terms from R. J. Mathar, Aug 17 2006