login
A number n is included if, for at least one distinct prime p dividing n, p+1 divides n.
1

%I #15 Dec 17 2022 15:32:45

%S 6,12,18,24,30,36,42,48,54,56,60,66,72,78,84,90,96,102,108,112,114,

%T 120,126,132,138,144,150,156,162,168,174,180,182,186,192,198,204,210,

%U 216,222,224,228,234,240,246,252,258,264,270,276,280,282,288,294,300,306

%N A number n is included if, for at least one distinct prime p dividing n, p+1 divides n.

%C The sequence contains all the positive multiples of 6.

%C Numbers not == 0 (mod 6): 56, 112, 182, 224, 280, 364, 380, 392, 448, 560, 616, 728, 760, 784, 896, 910, 952, 992, ..., . - _Robert G. Wilson v_

%H Harvey P. Dale, <a href="/A126798/b126798.txt">Table of n, a(n) for n = 1..1000</a>

%e The distinct primes that divide 56 are 2 and 7. 56 is included in the sequence because (7+1)=8 divides 56.

%p with(numtheory): a:=proc(n) local A,fsn,j: fsn:=factorset(n): A:={}: for j from 1 to nops(fsn) do if type(n/(1+fsn[j]),integer)=true then A:=A union {j} else A:=A: fi: od: if nops(A)>0 then n else fi end: seq(a(n),n=2..370); # _Emeric Deutsch_, Mar 28 2007

%t fQ[n_] := Block[{fi = First /@ FactorInteger@n + 1}, MemberQ[IntegerQ /@ (n/fi), True]]; Select[ Range@ 300, fQ@# &] (* _Robert G. Wilson v_ *)

%t Select[Range[400],Length[Intersection[FactorInteger[#][[All,1]]+1,Divisors[#]]]>0&] (* _Harvey P. Dale_, Dec 17 2022 *)

%K nonn

%O 1,1

%A _Leroy Quet_, Mar 14 2007

%E More terms from _Emeric Deutsch_, Mar 28 2007