A126798 - OEIS

A126798

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

6, 12, 18, 24, 30, 36, 42, 48, 54, 56, 60, 66, 72, 78, 84, 90, 96, 102, 108, 112, 114, 120, 126, 132, 138, 144, 150, 156, 162, 168, 174, 180, 182, 186, 192, 198, 204, 210, 216, 222, 224, 228, 234, 240, 246, 252, 258, 264, 270, 276, 280, 282, 288, 294, 300, 306

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OFFSET

1,1

COMMENTS

The sequence contains all the positive multiples of 6.

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

LINKS

Harvey P. Dale, Table of n, a(n) for n = 1..1000

EXAMPLE

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

MAPLE

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

MATHEMATICA

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

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

CROSSREFS

Sequence in context: A315771 A315772 A121827 * A175130 A008458 A008588

Adjacent sequences: A126795 A126796 A126797 * A126799 A126800 A126801

KEYWORD

nonn

AUTHOR

Leroy Quet, Mar 14 2007

EXTENSIONS

More terms from Emeric Deutsch, Mar 28 2007

STATUS

approved