cp's OEIS Frontend

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.

%I A383677 #108 Jun 18 2025 21:41:15
%S A383677 30,120,-1,1080,3135,3570,10336,10695,10626,-1,100672,102695,103730,
%T A383677 844305,-1,1003520,1005039,1003450,1218945,1231230,-1,10017286,
%U A383677 10000295,10003390,10064145,10314150,-1,100216924,100019275,100017216,100367745,100327920,463798335,-1
%N 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.
%C A383677 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].
%e A383677 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).
%e A383677 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).
%e A383677 Triangle begins:
%e A383677        30;
%e A383677       120,      -1;
%e A383677      1080,    3135,    3570;
%e A383677     10336,   10695,   10626,      -1;
%e A383677    100672,  102695,  103730,  844305,      -1;
%e A383677   1003520, 1005039, 1003450, 1218945, 1231230, -1;
%e A383677   ...
%Y A383677 Cf. A001221, A002110, A067175, A365795, A382469, A383725, A383726, A383728, A383729.
%K A383677 sign,tabf,base
%O A383677 2,1
%A A383677 _Jean-Marc Rebert_, May 11 2025