A120736 - OEIS

%I #40 Feb 18 2024 08:27:03

%S 1,2,6,8,9,10,12,14,18,22,24,26,30,34,36,38,40,42,46,54,56,58,60,62,

%T 66,70,72,74,78,80,82,84,86,88,90,94,96,102,104,106,108,110,114,118,

%U 120,122,126,128,130,132,134,136,138,142,146,150,152,154,156,158,166,168

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

%C Sequence is identical to A048751 except for terms 1 and 2 that are included here. - _Michel Marcus_, Jun 06 2014

%C Numbers k such that tau(k) = A000005(k) divides the product of the divisors of k (A007955). - _Jaroslav Krizek_, Sep 05 2017

%H Paolo P. Lava, <a href="/A120736/b120736.txt">Table of n, a(n) for n = 1..10000</a>

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

%p 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 ;

%p # _R. J. Mathar_, Aug 17 2006

%t Select[Range@ 168, Divisible[Times @@ Divisors@ #, DivisorSigma[0, #]] &] (* _Michael De Vlieger_, Sep 05 2017 *)

%o (Magma) [n: n in [1..1000] | Denominator(&*[d: d in Divisors(n)] / #[d: d in Divisors(n)]) eq 1];  // _Jaroslav Krizek_, Sep 05 2017

%Y Cf. A000005, A120737.

%K nonn

%O 1,2

%A _Leroy Quet_, Jun 29 2006

%E More terms from _R. J. Mathar_, Aug 17 2006