A266005 Numbers n = p_1^s_1...p_m^s_m such that (p_i^s_i - 1) | n for all 0<i<=m.

1, 2, 6, 12, 42, 60, 84, 156, 168, 240, 420, 504, 660, 720, 780, 840, 1092, 1200, 1404, 1680, 1806, 1860, 2184, 2436, 2520, 2640, 3120, 3600, 3612, 3660, 4032, 4080, 4200, 4620, 4872, 5040, 5460, 6480, 6552, 7020, 7224, 7440, 7920, 8268, 8400, 8580, 9240, 9360, 9576, 9828, 9840, 10920, 11760, 12180, 12240

Offset

1,2

Comments

From Robert Israel, Jan 06 2016: (Start)

All terms except 1 and 2 are divisible by 6.

The only squarefree terms are 1, 2, 6, 42, 1806. (End)

Links

Robert Israel, Table of n, a(n) for n = 1..4000

Example

60 is a term since 60 = 2^2*3*5 and is divisible by 2^2-1, 3-1 and 5-1.

Maple

filter:= proc(n) local t;
    for t in ifactors(n)[2] do
      if n mod (t[1]^t[2]-1) <> 0 then return false fi
    od;
    true
end proc:
select(filter, [$1..10^5]); # Robert Israel, Jan 06 2016

Mathematica

fa=FactorInteger; G[n_] := Union@Table[IntegerQ[n/(fa[n][[i, 1]]^fa[n][[i, 2]] - 1)], {i, Length[fa[n]]}] === {True}; Select[Range[20000], G]

Prog

(PARI) isok(n) = {my(f = factor(n)); for (k=1, #f~, if ((n % (f[k, 1]^f[k, 2]-1)), return (0)); ); return (1); } \\ Michel Marcus, Jan 04 2016

Crossrefs

Sequence in context: A080497 A127724 A178008 * A056744 A344184 A164859

Adjacent sequences: A266002 A266003 A266004 * A266006 A266007 A266008

Keyword

nonn

Author

José María Grau Ribas, Dec 20 2015

Status

approved