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 A027750 Triangle read by rows in which row n lists the divisors of n. 393
 1, 1, 2, 1, 3, 1, 2, 4, 1, 5, 1, 2, 3, 6, 1, 7, 1, 2, 4, 8, 1, 3, 9, 1, 2, 5, 10, 1, 11, 1, 2, 3, 4, 6, 12, 1, 13, 1, 2, 7, 14, 1, 3, 5, 15, 1, 2, 4, 8, 16, 1, 17, 1, 2, 3, 6, 9, 18, 1, 19, 1, 2, 4, 5, 10, 20, 1, 3, 7, 21, 1, 2, 11, 22, 1, 23, 1, 2, 3, 4, 6, 8, 12, 24, 1, 5, 25, 1, 2, 13, 26, 1, 3, 9, 27, 1, 2, 4, 7, 14, 28, 1, 29 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Or, in the list of natural numbers (A000027), replace n with its divisors. This gives the first elements of the ordered pairs (a,b) a >= 1, b >= 1 ordered by their product ab. Also, row n lists the largest parts of the partitions of n whose parts are not distinct. - Omar E. Pol, Sep 17 2008 Concatenation of n-th row gives A037278(n). - Reinhard Zumkeller, Aug 07 2011 {A210208(n,k): k=1..A073093(n)} subset of {T(n,k): k=1..A000005(n)} for all n. - Reinhard Zumkeller, Mar 18 2012 Row sums give A000203. Right border gives A000027. - Omar E. Pol, Jul 29 2012 Indices of records are in A006218. - Irina Gerasimova, Feb 27 2013 The number of primes in the n-th row is omega(n) = A001221(n). - Michel Marcus, Oct 21 2015 The row polynomials P(n,x) = Sum_{k=1..A000005(n)} T(n,k)*x^k with composite n which are irreducible over the integers are given in A292226. - Wolfdieter Lang, Nov 09 2017 T(n,k) is also the number of parts in the k-th partition of n into equal parts (see example). - Omar E. Pol, Nov 20 2019 LINKS Franklin T. Adams-Watters, Rows 1..1000, flattened Franklin T. Adams-Watters, Rows 1..10000 Omar E. Pol, Illustration of initial terms, (2009). Eric Weisstein's World of Mathematics, Divisor Wikipedia, Table of divisors FORMULA a(A006218(n-1) + k) = k-divisor of n, 1 <= k <= A000005(n). - Reinhard Zumkeller, May 10 2006 T(n,k) = n / A056538(n,k) = A056538(n,n-k+1), 1 <= k <= A000005(n). - Reinhard Zumkeller, Sep 28 2014 EXAMPLE Triangle begins: 1; 1, 2; 1, 3; 1, 2, 4; 1, 5; 1, 2, 3, 6; 1, 7; 1, 2, 4, 8; 1, 3, 9; 1, 2, 5, 10; 1, 11; 1, 2, 3, 4, 6, 12; ... For n = 6 the partitions of 6 into equal parts are [6], [3,3], [2,2,2], [1,1,1,1,1,1], so the number of parts are [1, 2, 3, 6] respectively, the same as the divisors of 6. - Omar E. Pol, Nov 20 2019 MAPLE seq(op(numtheory:-divisors(a)), a = 1 .. 20) # Matt C. Anderson, May 15 2017 MATHEMATICA Flatten[ Table[ Flatten [ Divisors[ n ] ], {n, 1, 30} ] ] PROG (MAGMA) [Divisors(n) : n in [1..20]]; (Haskell) a027750 n k = a027750_row n !! (k-1) a027750_row n = filter ((== 0) . (mod n)) [1..n] a027750_tabf = map a027750_row [1..] -- Reinhard Zumkeller, Jan 15 2011, Oct 21 2010 (PARI) v=List(); for(n=1, 20, fordiv(n, d, listput(v, d))); Vec(v) \\ Charles R Greathouse IV, Apr 28 2011 (Python) from sympy import divisors for n in range(1, 16):     print(divisors(n)) # Indranil Ghosh, Mar 30 2017 CROSSREFS Cf. A000005 (row length), A001221, A027749, A027751, A056534, A056538, A127093, A135010, A161700, A163280, A240698 (partial sums of rows), A240694 (partial products of rows), A247795 (parities), A292226, A244051. Sequence in context: A210208 A162306 A233773 * A275055 A254679 A275280 Adjacent sequences:  A027747 A027748 A027749 * A027751 A027752 A027753 KEYWORD nonn,easy,tabf,look AUTHOR EXTENSIONS More terms from Scott Lindhurst (ScottL(AT)alumni.princeton.edu) STATUS approved

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Last modified October 19 12:00 EDT 2020. Contains 337880 sequences. (Running on oeis4.)