A383677 Irregular triangle read by rows: T(n,k), 2 <= n , 3 <= k <= largest k such that A067175(k) <= n , is the smallest n-digit number m such that omega(m) = A001221(m) = k, and its largest prime factor equals the sum of its remaining prime factors. or -1 if no such number exists.

30, 120, -1, 1080, 3135, 3570, 10336, 10695, 10626, -1, 100672, 102695, 103730, 844305, -1, 1003520, 1005039, 1003450, 1218945, 1231230, -1, 10017286, 10000295, 10003390, 10064145, 10314150, -1, 100216924, 100019275, 100017216, 100367745, 100327920, 463798335, -1

Offset: 2

Author

Jean-Marc Rebert, May 11 2025

Keywords

• sign
• tabf
• base

Comments

For n ranging from 2 to 20, the corresponding maximum values of k are as follows: [3, 4, 5, 6, 7, 8, 8, 9, 10, 10, 11, 12, 12, 13, 13, 14, 15, 15, 16].

Examples

			T(4,3) = 1080 is the smallest 4-digit number having 3 distinct prime factors (namely 2, 3, and 5) such that the largest one is the sum of the others (2 + 3 = 5).
T(5,4) = 10695 is the smallest 5-digit number having 4 distinct prime factors (namely 3, 5, 23 and 31) such that the largest one is the sum of the others (3 + 5 + 23 = 31).
Triangle begins:
       30;
      120,      -1;
     1080,    3135,    3570;
    10336,   10695,   10626,      -1;
   100672,  102695,  103730,  844305,      -1;
  1003520, 1005039, 1003450, 1218945, 1231230, -1;
  ...
		

Crossrefs

Cf. A001221, A002110, A067175, A365795, A382469, A383725, A383726, A383728, A383729.