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A276674 Numbers n such that x - lambda(x) = n has no solution, where lambda(x) = A002322(x).

%I A276674 #51 Apr 27 2017 23:18:00
%S A276674 21,28,45,46,51,64,65,77,82,85,91,106,111,126,129,133,136,148,155,166,
%T A276674 172,175,185,189,205,208,209,217,221,225,231,232,235,237,244,247,267,
%U A276674 273,274,276,286,291,298,305,316,319,326,333,339,341,358,362,364,365,371
%N A276674 Numbers n such that x - lambda(x) = n has no solution, where lambda(x) = A002322(x).
%C A276674 Problem: are there infinitely many such numbers?
%C A276674 Note that all these numbers are composite, because p - lambda(p) = 1 and p^2 - lambda(p^2) = p prime.
%C A276674 If x - lambda(x) = n > 1, then x <= n^2.
%C A276674 Conjecture: if x - lambda(x) = 2*m > 0, then x <= 4*m.
%C A276674 Noncototients among these numbers are 172, 232, 244, 274, 298, 326, 362, ...
%o A276674 (PARI) lista(nn) = {v = vecsort(vector(nn^2, n, n - lcm(znstar(n)[2])), ,8); for (n=1, nn, if (! vecsearch(v, n), print1(n, ", ")););} \\ _Michel Marcus_, Oct 03 2016
%o A276674 (Perl) use ntheory ":all"; sub A { my $l=shift; my %C; undef $C{$_-carmichael_lambda($_)} for 1..$l*$l; my @R = grep { !exists $C{$_} } 1..$l; @R; } say for A(500); # _Dana Jacobsen_, Apr 27 2017
%Y A276674 Cf. A002322, A005278 (see links). Complement of A277127.
%K A276674 nonn
%O A276674 1,1
%A A276674 _Thomas Ordowski_, Oct 03 2016
%E A276674 More terms from _Michel Marcus_, Oct 03 2016