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A249819 Composite natural numbers n for which there are exactly two distinct 0 < k < n^2 such that 2^k - 1 is divisible by n^2.

%I A249819 #12 Nov 16 2014 14:42:05
%S A249819 35,49,77,95,115,143,175,209,235,245,289,295,299,319,335,343,371,395,
%T A249819 407,413,415,437,475,515,517,529,535,539,551,575,581,583,611,649,667,
%U A249819 695,707,749,767,815,835,847,851,869,875,893,895,913,917,923,995,1007
%N A249819 Composite natural numbers n for which there are exactly two distinct 0 < k < n^2 such that 2^k - 1 is divisible by n^2.
%C A249819 Equally: odd composite numbers n for which A246702((n+1)/2) = 2.
%e A249819 35 = 5*7 is an odd composite. Only cases where 2^k - 1 (with k in range 1 .. 35^2 - 1 = 1 .. 1224) is a multiple of 35 are k = 420 and k = 840, thus 35 is included in this sequence.
%p A249819 isA249819 := proc(n)
%p A249819     if isprime(n) or n=1 then
%p A249819         false;
%p A249819     else
%p A249819         ct := 0 ;
%p A249819         for k from 1 to n^2-1 do
%p A249819             if modp(2 &^ k-1,n^2) = 0 then
%p A249819                 ct := ct+1 ;
%p A249819             end if;
%p A249819             if ct > 2 then
%p A249819                 return false;
%p A249819             end if;
%p A249819         end do:
%p A249819         return is(ct=2) ;
%p A249819     end if;
%p A249819 end proc:
%p A249819 for n from 1 to 1100 do
%p A249819     if isA249819(n) then
%p A249819         printf("%d,\n",n) ;
%p A249819     end if;
%p A249819 end do: # _R. J. Mathar_, Nov 16 2014
%o A249819 (Scheme, with _Antti Karttunen_'s IntSeq-library)
%o A249819 (define A249819 (MATCHING-POS 1 1 (lambda (n) (and (odd? n) (not (prime? n)) (= 2 (A246702 (/ (+ 1 n) 2)))))))
%Y A249819 Composite terms in A246717.
%Y A249819 Seems also to be a subsequence of A038509.
%Y A249819 Cf. A246702.
%K A249819 nonn
%O A249819 1,1
%A A249819 _Antti Karttunen_, Nov 15 2014