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.

35, 49, 77, 95, 115, 143, 175, 209, 235, 245, 289, 295, 299, 319, 335, 343, 371, 395, 407, 413, 415, 437, 475, 515, 517, 529, 535, 539, 551, 575, 581, 583, 611, 649, 667, 695, 707, 749, 767, 815, 835, 847, 851, 869, 875, 893, 895, 913, 917, 923, 995, 1007

Offset

1,1

Comments

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

Links

Table of n, a(n) for n=1..52.

Example

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.

Maple

isA249819 := proc(n)
    if isprime(n) or n=1 then
        false;
    else
        ct := 0 ;
        for k from 1 to n^2-1 do
            if modp(2 &^ k-1, n^2) = 0 then
                ct := ct+1 ;
            end if;
            if ct > 2 then
                return false;
            end if;
        end do:
        return is(ct=2) ;
    end if;
end proc:
for n from 1 to 1100 do
    if isA249819(n) then
        printf("%d, \n", n) ;
    end if;
end do: # R. J. Mathar, Nov 16 2014

Prog

(Scheme, with Antti Karttunen's IntSeq-library)
(define A249819 (MATCHING-POS 1 1 (lambda (n) (and (odd? n) (not (prime? n)) (= 2 (A246702 (/ (+ 1 n) 2)))))))

Crossrefs

Composite terms in A246717.

Seems also to be a subsequence of A038509.

Cf. A246702.

Sequence in context: A034115 A212600 A247135 * A186319 A248659 A089268

Adjacent sequences: A249816 A249817 A249818 * A249820 A249821 A249822

Keyword

nonn

Author

Antti Karttunen, Nov 15 2014

Status

approved