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%I #18 Mar 23 2021 05:18:43
%S 1,2,3,5,7,11,13,17,19,21,23,27,29,31,36,37,40,41,43,44,46,47,53,59,
%T 61,66,67,70,71,73,79,83,89,97,101,103,107,109,113,127,131,137,139,
%U 149,151,157,163,167,173,179,181,191,193,197,199,207,211,219,223,227,229,231
%N Numbers k for which the cototient k-phi(k) is an enneagonal number (A001106).
%H Robert Israel, <a href="/A117289/b117289.txt">Table of n, a(n) for n = 1..10000</a>
%e 44 is in the sequence because 44-phi(44) = 24, which is an enneagonal number.
%p N:= 1000: # to get all terms <= N
%p enneagonal:= [seq(n*(7*n-5)/2, n=0..floor((sqrt(25+56*N)+5)/14))]:
%p select(t -> member(t - numtheory:-phi(t), enneagonal), [$1..N]); # _Robert Israel_, Mar 30 2018
%t ennQ[n_] := n == 0 || IntegerQ[(Sqrt[56*n + 25] + 5)/14]; Select[Range[250], ennQ[# - EulerPhi[#]] &] (* _Amiram Eldar_, Mar 23 2021 *)
%o (PARI) isok(n) = ispolygonal(n - eulerphi(n), 9); \\ _Michel Marcus_, Feb 26 2014
%Y Cf. A000010, A001106, A051953.
%Y Cf. A117283, A117284, A117285, A117286, A117287, A117288.
%K nonn
%O 1,2
%A Luc Stevens (lms022(AT)yahoo.com), Apr 23 2006
%E Offset changed to 1 by _Robert Israel_, Mar 30 2018
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