# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a027750 Showing 1-1 of 1 %I A027750 #115 Mar 27 2024 13:06:12 %S A027750 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, %T A027750 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, %U A027750 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 %N A027750 Triangle read by rows in which row n lists the divisors of n. %C A027750 Or, in the list of natural numbers (A000027), replace n with its divisors. %C A027750 This gives the first elements of the ordered pairs (a,b) a >= 1, b >= 1 ordered by their product ab. %C A027750 Also, row n lists the largest parts of the partitions of n whose parts are not distinct. - _Omar E. Pol_, Sep 17 2008 %C A027750 Concatenation of n-th row gives A037278(n). - _Reinhard Zumkeller_, Aug 07 2011 %C A027750 {A210208(n,k): k=1..A073093(n)} subset of {T(n,k): k=1..A000005(n)} for all n. - _Reinhard Zumkeller_, Mar 18 2012 %C A027750 Row sums give A000203. Right border gives A000027. - _Omar E. Pol_, Jul 29 2012 %C A027750 Indices of records are in A006218. - _Irina Gerasimova_, Feb 27 2013 %C A027750 The number of primes in the n-th row is omega(n) = A001221(n). - _Michel Marcus_, Oct 21 2015 %C A027750 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 %C A027750 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 %H A027750 Franklin T. Adams-Watters, Rows 1..1000, flattened %H A027750 Franklin T. Adams-Watters, Rows 1..10000 %H A027750 Omar E. Pol, Illustration of initial terms, (2009). %H A027750 Eric Weisstein's World of Mathematics, Divisor %H A027750 Wikipedia, Table of divisors %H A027750 Index entries for sequences related to divisors of numbers %F A027750 a(A006218(n-1) + k) = k-divisor of n, 1 <= k <= A000005(n). - _Reinhard Zumkeller_, May 10 2006 %F A027750 T(n,k) = n / A056538(n,k) = A056538(n,n-k+1), 1 <= k <= A000005(n). - _Reinhard Zumkeller_, Sep 28 2014 %e A027750 Triangle begins: %e A027750 1; %e A027750 1, 2; %e A027750 1, 3; %e A027750 1, 2, 4; %e A027750 1, 5; %e A027750 1, 2, 3, 6; %e A027750 1, 7; %e A027750 1, 2, 4, 8; %e A027750 1, 3, 9; %e A027750 1, 2, 5, 10; %e A027750 1, 11; %e A027750 1, 2, 3, 4, 6, 12; %e A027750 ... %e A027750 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 %p A027750 seq(op(numtheory:-divisors(a)), a = 1 .. 20) # _Matt C. Anderson_, May 15 2017 %t A027750 Flatten[ Table[ Flatten [ Divisors[ n ] ], {n, 1, 30} ] ] %o A027750 (Magma) [Divisors(n) : n in [1..20]]; %o A027750 (Haskell) %o A027750 a027750 n k = a027750_row n !! (k-1) %o A027750 a027750_row n = filter ((== 0) . (mod n)) [1..n] %o A027750 a027750_tabf = map a027750_row [1..] %o A027750 -- _Reinhard Zumkeller_, Jan 15 2011, Oct 21 2010 %o A027750 (PARI) v=List();for(n=1,20,fordiv(n,d,listput(v,d)));Vec(v) \\ _Charles R Greathouse IV_, Apr 28 2011 %o A027750 (Python) %o A027750 from sympy import divisors %o A027750 for n in range(1, 16): %o A027750 print(divisors(n)) # _Indranil Ghosh_, Mar 30 2017 %Y A027750 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. %K A027750 nonn,easy,tabf,look %O A027750 1,3 %A A027750 _N. J. A. Sloane_ %E A027750 More terms from Scott Lindhurst (ScottL(AT)alumni.princeton.edu) # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE