|
| |
|
|
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
|
| |
|
|
