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%I #32 Jul 22 2021 23:26:10
%S 4147,8294,8323,12441,16646,20735,24882,24969,41470,41615,49938,55309,
%T 62205,83230,91553,108199,110618,124410,124845,165927,183106,216398,
%U 249690,274659,276545,324597,331854,387163,457765,540995,549318,553090,608399,649194,719017,774326,829635,915530
%N Squarefree numbers k such that alpha(k) = lambda(k), where alpha(k) = LCM of all (p+1) for primes p dividing k, and lambda(k) = A002322(k).
%C Are there infinitely many such numbers?
%C These numbers have at least three prime factors.
%C If m and k are in the sequence, then lcm(m,k) is in the sequence. - _Robert Israel_, Jul 05 2017
%H Robert G. Wilson v, <a href="/A287514/b287514.txt">Table of n, a(n) for n = 1..398</a>
%e 4147 = 11*13*29 and lcm(12,14,30) = lcm(10,12,28) = 420.
%e 13*23*29*41*43 multiplied by any divisor of 2*3*5*7*11.
%p filter:= proc(n) local F;
%p F:= ifactors(n)[2];
%p if max(seq(f[2],f=F)) > 1 then return false fi;
%p ilcm(seq(f[1]-1, f=F)) = ilcm(seq(f[1]+1, f=F))
%p end proc:
%p select(filter, [$2..10^6]); # _Robert Israel_, Jul 05 2017
%t fQ[n_] := If[ SquareFreeQ@ n, Block[{p = First@ Transpose@ FactorInteger@ n}, LCM @@ (p - 1) == LCM @@ (p + 1)], False]; Select[ Range[10^6], fQ] (* _Robert G. Wilson v_, Jun 05 2017 *)
%Y Cf. A002322.
%K nonn
%O 1,1
%A _Thomas Ordowski_, May 26 2017
%E More terms from _Robert G. Wilson v_, Jun 05 2017
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