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A120736
Numbers k such that every prime p that divides d(k) (A000005) also divides k.
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
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
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
Sequence in context: A077477 A095879 A342751 * A130099 A047397 A174331
KEYWORD
nonn
AUTHOR
Leroy Quet, Jun 29 2006
EXTENSIONS
More terms from R. J. Mathar, Aug 17 2006
STATUS
approved