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A266005 Numbers n = p_1^s_1...p_m^s_m such that (p_i^s_i - 1) | n for all 0<i<=m. 4

%I

%S 1,2,6,12,42,60,84,156,168,240,420,504,660,720,780,840,1092,1200,1404,

%T 1680,1806,1860,2184,2436,2520,2640,3120,3600,3612,3660,4032,4080,

%U 4200,4620,4872,5040,5460,6480,6552,7020,7224,7440,7920,8268,8400,8580,9240,9360,9576,9828,9840,10920,11760,12180,12240

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

%C From _Robert Israel_, Jan 06 2016: (Start)

%C All terms except 1 and 2 are divisible by 6.

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

%H Robert Israel, <a href="/A266005/b266005.txt">Table of n, a(n) for n = 1..4000</a>

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

%p filter:= proc(n) local t;

%p for t in ifactors(n)[2] do

%p if n mod (t[1]^t[2]-1) <> 0 then return false fi

%p od;

%p true

%p end proc:

%p select(filter, [$1..10^5]); # _Robert Israel_, Jan 06 2016

%t 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]

%o (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

%K nonn

%O 1,2

%A _José María Grau Ribas_, Dec 20 2015

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Last modified October 26 21:33 EDT 2021. Contains 348269 sequences. (Running on oeis4.)