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A118854 Numbers m such that m-1 and m have the same number of common totatives as m and m+1 have.

%I A118854 #5 Feb 16 2025 08:33:01
%S A118854 2,3,8,21,24,27,45,75,93,105,117,123,147,165,213,309,315,333,357,387,
%T A118854 453,525,555,573,627,636,693,717,729,765,795,843,915,933,957,1005,
%U A118854 1083,1125,1173,1227,1323,1347,1437,1467,1515,1563,1575,1677,1725,1755,1773
%N A118854 Numbers m such that m-1 and m have the same number of common totatives as m and m+1 have.
%C A118854 A057475(a(n)-1) = A057475(a(n));
%C A118854 it seems that even values are very rare, see A118855.
%H A118854 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Totative.html">Totative</a>
%e A118854 n = 21, the sets of totatives for 21-1, 21 and 21+1:
%e A118854 T(20) = {1,3,7,9,11,13,17,19},
%e A118854 T(21) = {1,2,4,5,8,10,11,13,16,17,19,20},
%e A118854 T(22) = {1,3,5,7,9,13,15,17,19,21},
%e A118854 A057475(20) = #intersect(T(20),T(21)) = #{1,11,13,17,19} = 5,
%e A118854 A057475(20) = #intersect(T(21),T(22)) = #{1,5,13,17,19} = 5,
%e A118854 therefore 21 is a term.
%K A118854 nonn
%O A118854 1,1
%A A118854 _Reinhard Zumkeller_, May 02 2006