A390494 - OEIS

A390494

Irregular triangle read by rows: T(n,k) is the sum of nonprime numbers in the k-th 2-dense sublist of divisors of n, with n >= 1, k >= 1.

%I #20 Nov 19 2025 09:59:37

%S 1,1,1,0,5,1,0,7,1,0,13,1,0,9,1,10,1,0,23,1,0,1,14,1,0,15,29,1,0,34,1,

%T 0,35,1,0,0,21,1,22,1,0,55,1,0,25,1,26,1,0,9,27,47,1,0,62,1,0,61,1,0,

%U 0,33,1,34,1,0,35,86,1,0,1,38,1,0,0,39,83,1,0,84,1,0,5,66,1,24,45,1,46,1,0,119,1,0,49

%N Irregular triangle read by rows: T(n,k) is the sum of nonprime numbers in the k-th 2-dense sublist of divisors of n, with n >= 1, k >= 1.

%C In a sublist of divisors of n the terms are in increasing order and two adjacent terms are the same two adjacent terms in the list of divisors of n.

%C The 2-dense sublists of divisors of n are the maximal sublists whose terms increase by a factor of at most 2.

%C At least for the first 1000 rows the row lengths give A237271.

%H Paolo Xausa, <a href="/A390494/b390494.txt">Table of n, a(n) for n = 1..10607</a> (rows 1..3500 of triangle, flattened).

%F T(n,k) = A384149(n,k) - A390495(n,k).

%e --------------------------------------------------------------------

%e | n | Row n of | List of divisors of n | Number of |

%e --------------------------------------------------------------------

%e | 1 | 1; | [1]; | 1 |

%e | 2 | 1; | [1, 2]; | 1 |

%e | 3 | 1, 0; | [1], [3]; | 2 |

%e | 4 | 5; | [1, 2, 4]; | 1 |

%e | 5 | 1, 0; | [1], [5]; | 2 |

%e | 6 | 7; | [1, 2, 3, 6]; | 1 |

%e | 7 | 1, 0; | [1], [7]; | 2 |

%e | 8 | 13; | [1, 2, 4, 8]; | 1 |

%e | 9 | 1, 0, 9; | [1], [3], [9]; | 3 |

%e | 10 | 1, 10; | [1, 2], [5, 10]; | 2 |

%e | 11 | 1, 0; | [1], [11]; | 2 |

%e | 12 | 23; | [1, 2, 3, 4, 6, 12]; | 1 |

%e | 13 | 1, 0; | [1], [13]; | 2 |

%e | 14 | 1, 14; | [1, 2], [7, 14]; | 2 |

%e | 15 | 1, 0, 15; | [1], [3, 5], [15]; | 3 |

%e | 16 | 29; | [1, 2, 4, 8, 16]; | 1 |

%e | 17 | 1, 0; | [1], [17]; | 2 |

%e | 18 | 34; | [1, 2, 3, 6, 9, 18]; | 1 |

%e | 19 | 1, 0; | [1], [19]; | 2 |

%e | 20 | 35; | [1, 2, 4, 5, 10, 20]; | 1 |

%e | 21 | 1, 0, 0, 21; | [1], [3], [7], [21]; | 4 |

%e ...

%e For n = 78 the list of divisors of 78 is [1, 2, 3, 6, 13, 26, 39, 78]. There are two 2-dense sublists of divisors of 78, they are [1, 2, 3, 6] and [13, 26, 39, 78]. In the first 2-dense sublist the sum of nonprime numbers is 1 + 6 = 7, so T(78,1) = 7. In the second 2-dense sublist the sum of nonprime numbers is 26 + 39 + 78 = 143, so T(78,2) = 143.

%t A390494row[n_] := Map[Total[Select[#, !PrimeQ[#] &]] &, Split[Divisors[n], #2 <= 2*# &]];

%t Array[A390494row, 50] (* _Paolo Xausa_, Nov 18 2025 *)

%Y Row sums give A023890.

%Y Cf. A018252, A027750, A174973 (2-dense numbers), A237271, A379288, A384149, A384222, A384225, A384226, A386604, A386989, A386992, A387030, A389592, A389761, A389762, A390443, A390495.

%K nonn,tabf

%O 1,5

%A _Omar E. Pol_, Nov 11 2025