The OEIS is supported by the many generous donors to the OEIS Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A224613 a(n) = sigma(6*n). 26
 12, 28, 39, 60, 72, 91, 96, 124, 120, 168, 144, 195, 168, 224, 234, 252, 216, 280, 240, 360, 312, 336, 288, 403, 372, 392, 363, 480, 360, 546, 384, 508, 468, 504, 576, 600, 456, 560, 546, 744, 504, 728, 528, 720, 720, 672, 576, 819, 684, 868, 702, 840, 648 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Conjectures: sigma(6n) > sigma(6n - 1) and sigma(6n) > sigma(6n + 1). Conjectures are false. Try prime 73961483429 for n. One finds sigma(6*73961483429) < sigma(6*73961483429+1). The number n = 105851369791 provides a counterexample for the other case. - T. D. Noe, Apr 22 2013 Sum of the divisors of the numbers k which have the property that the width associated to the vertex of the first (also the last) valley of the smallest Dyck path of the symmetric representation of sigma(k) is equal to 2 (see example). Other positive integers have width 0 or 1 associated to the mentioned valley. - Omar E. Pol, Aug 11 2021 LINKS Seiichi Manyama, Table of n, a(n) for n = 1..10000 FORMULA a(n) = A000203(6n). a(n) = A000203(A008588(n)). - Omar E. Pol, Aug 11 2021 EXAMPLE From Omar E. Pol, Aug 11 2021: (Start) Illustration of initial terms: ----------------------------------------------------------------------    n    6*n   a(n)    Diagram:  1           2           3           4 ----------------------------------------------------------------------                                 _           _           _           _                                | |         | |         | |         | |                                | |         | |         | |         | |                           * _ _| |         | |         | |         | |                            |  _ _|         | |         | |         | |                       _ _ _| |_|           | |         | |         | |    1     6     12    |_ _ _ _|      * _ _ _| |         | |         | |                                     _|  _ _ _|         | |         | |                                 * _|  _| |             | |         | |                                  |  _|  _|    * _ _ _ _| |         | |                                  | |_ _|       |  _ _ _ _|         | |                       _ _ _ _ _ _| |          _| | |               | |    2    12     28    |_ _ _ _ _ _ _|        _|  _|_|    * _ _ _ _ _| |                                       * _ _|  _|         |  _ _ _ _ _|                                        |  _ _|        _ _| | |                                        | |_ _|      _|  _ _| |                                        | |        _|  _|  _ _|                       _ _ _ _ _ _ _ _ _| |       |  _|  _|    3    18     39    |_ _ _ _ _ _ _ _ _ _|  * _ _| |  _|                                              |  _ _| |                                              | |_ _ _|                                              | |                                              | |                       _ _ _ _ _ _ _ _ _ _ _ _| |    4    24     60    |_ _ _ _ _ _ _ _ _ _ _ _ _| . Note that the mentioned vertices are aligned on two straight lines that meet at point (3,3). a(n) equals the area (also the number of cells) in the n-th diagram. (End) MATHEMATICA DivisorSigma[1, 6*Range] (* Harvey P. Dale, Apr 16 2016 *) PROG (PARI) a(n)=sigma(6*n) \\ Charles R Greathouse IV, Apr 22 2013 (Python) from sympy import divisor_sigma def a(n):  return divisor_sigma(6*n) print([a(n) for n in range(1, 54)]) # Michael S. Branicky, Dec 28 2021 CROSSREFS Sigma(k*n): A000203 (k=1), A062731 (k=2), A144613 (k=3), A193553 (k=4), this sequence (k=6), A283078 (k=7). Cf. A000203 (sigma(n)), A053224 (n: sigma(n) < sigma(n+1)). Cf. A067825 (even n: sigma(n)< sigma(n+1)). Cf. A008588, A237593. Sequence in context: A255136 A087252 A141274 * A134618 A108405 A184838 Adjacent sequences:  A224610 A224611 A224612 * A224614 A224615 A224616 KEYWORD nonn AUTHOR Zak Seidov, Apr 22 2013 EXTENSIONS Corrected by Harvey P. Dale, Apr 16 2016 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified August 18 19:12 EDT 2022. Contains 356215 sequences. (Running on oeis4.)