A249819 - OEIS

%I #12 Nov 16 2014 14:42:05

%S 35,49,77,95,115,143,175,209,235,245,289,295,299,319,335,343,371,395,

%T 407,413,415,437,475,515,517,529,535,539,551,575,581,583,611,649,667,

%U 695,707,749,767,815,835,847,851,869,875,893,895,913,917,923,995,1007

%N 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 Equally: odd composite numbers n for which A246702((n+1)/2) = 2.

%e 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 isA249819 := proc(n)

%p     if isprime(n) or n=1 then

%p         false;

%p     else

%p         ct := 0 ;

%p         for k from 1 to n^2-1 do

%p             if modp(2 &^ k-1,n^2) = 0 then

%p                 ct := ct+1 ;

%p             end if;

%p             if ct > 2 then

%p                 return false;

%p             end if;

%p         end do:

%p         return is(ct=2) ;

%p     end if;

%p end proc:

%p for n from 1 to 1100 do

%p     if isA249819(n) then

%p         printf("%d,\n",n) ;

%p     end if;

%p end do: # _R. J. Mathar_, Nov 16 2014

%o (Scheme, with _Antti Karttunen_'s IntSeq-library)

%o (define A249819 (MATCHING-POS 1 1 (lambda (n) (and (odd? n) (not (prime? n)) (= 2 (A246702 (/ (+ 1 n) 2)))))))

%Y Composite terms in A246717.

%Y Seems also to be a subsequence of A038509.

%Y Cf. A246702.

%K nonn

%O 1,1

%A _Antti Karttunen_, Nov 15 2014