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 A063440 Number of divisors of n-th triangular number. 13
 1, 2, 4, 4, 4, 4, 6, 9, 6, 4, 8, 8, 4, 8, 16, 8, 6, 6, 8, 16, 8, 4, 12, 18, 6, 8, 16, 8, 8, 8, 10, 20, 8, 8, 24, 12, 4, 8, 24, 12, 8, 8, 8, 24, 12, 4, 16, 24, 9, 12, 16, 8, 8, 16, 24, 24, 8, 4, 16, 16, 4, 12, 36, 24, 16, 8, 8, 16, 16, 8, 18, 18, 4, 12, 24, 16, 16, 8, 16, 40, 10, 4, 16 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS a(n) = 4 iff either n is in A005383 or n/2 is in A005384. a(n) is odd iff n is in A001108. a(n) = 6 if either n = 18 or n = q^2 where q is in A048161 or n = 2 q^2 - 1 where q is in A106483. - Robert Israel, Oct 26 2015 LINKS Ray Chandler, Table of n, a(n) for n=1..10000 FORMULA a(n) = A000005(A000217(n)). From Robert Israel, Oct 26 2015: (Start) a(2k) = A000005(k)*A000005(2k+1). a(2k+1) = A000005(2k+1)*A000005(k+1). gcd(a(2k), a(2k+1)) = A000005(2k+1) * A060778(k). (End) EXAMPLE a(6) = 4 since 1+2+3+4+5+6 = 21 has four divisors {1,3,7,21}. MAPLE seq(numtheory:-tau(n*(n+1)/2), n=1..100); # Robert Israel, Oct 26 2015 MATHEMATICA DivisorSigma[0, #]&/@Accumulate[Range] (* Harvey P. Dale, Apr 15 2019 *) PROG (PARI) for (n=1, 10000, write("b063440.txt", n, " ", numdiv(n*(n + 1)/2)) ) \\ Harry J. Smith, Aug 21 2009 (PARI) a(n)=factorback(apply(numdiv, if(n%2, [n, (n+1)/2], [n/2, n+1]))) \\ Charles R Greathouse IV, Dec 27 2014 (PARI) vector(100, n, numdiv(n*(n+1)/2)) \\ Altug Alkan, Oct 26 2015 CROSSREFS Cf. A000005, A000217. Cf. A001108, A005383, A005384, A048161, A060778, A081978, A106483. Sequence in context: A302254 A160409 A035645 * A008497 A220497 A194443 Adjacent sequences:  A063437 A063438 A063439 * A063441 A063442 A063443 KEYWORD nonn,easy AUTHOR Henry Bottomley, Jul 24 2001 STATUS approved

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Last modified May 19 06:41 EDT 2019. Contains 323386 sequences. (Running on oeis4.)