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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.
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.
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
KEYWORD
nonn
AUTHOR
Antti Karttunen, Nov 15 2014
STATUS
approved