cp's OEIS Frontend

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

%I A120736 #40 Feb 18 2024 08:27:03
%S A120736 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 A120736 66,70,72,74,78,80,82,84,86,88,90,94,96,102,104,106,108,110,114,118,
%U A120736 120,122,126,128,130,132,134,136,138,142,146,150,152,154,156,158,166,168
%N A120736 Numbers k such that every prime p that divides d(k) (A000005) also divides k.
%C A120736 Sequence is identical to A048751 except for terms 1 and 2 that are included here. - _Michel Marcus_, Jun 06 2014
%C A120736 Numbers k such that tau(k) = A000005(k) divides the product of the divisors of k (A007955). - _Jaroslav Krizek_, Sep 05 2017
%H A120736 Paolo P. Lava, <a href="/A120736/b120736.txt">Table of n, a(n) for n = 1..10000</a>
%e A120736 d(26) = 4. 2 is the only prime dividing 4. 2 divides 26, so 26 is in the sequence.
%p A120736 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 A120736 # _R. J. Mathar_, Aug 17 2006
%t A120736 Select[Range@ 168, Divisible[Times @@ Divisors@ #, DivisorSigma[0, #]] &] (* _Michael De Vlieger_, Sep 05 2017 *)
%o A120736 (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 A120736 Cf. A000005, A120737.
%K A120736 nonn
%O A120736 1,2
%A A120736 _Leroy Quet_, Jun 29 2006
%E A120736 More terms from _R. J. Mathar_, Aug 17 2006