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

1,2

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

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

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