cp's OEIS Frontend

A382364 a(n) is the smallest squarefree number k such that the sum of the digit counts of the prime factors of k equals the sum of n and the digit count of k.

%I A382364 #54 Jul 23 2025 16:07:40
%S A382364 6,66,858,72930,6374082,643782282,66309575046
%N A382364 a(n) is the smallest squarefree number k such that the sum of the digit counts of the prime factors of k equals the sum of n and the digit count of k.
%e A382364 a(1) = 6 = 2*3, because the total number of digits in its distinct prime factors (2 and 3) is 2. This equals the sum of n = 1 and the number of digits in 6, which is 1, and no lesser number has this property.
%e A382364 a(2) = 66 = 2*3*11, because the total number of digits in its distinct prime factors (2, 3 and 11) is 4. This equals the sum of n = 2 and the number of digits in 66, which is 2, and no lesser number has this property.
%e A382364 Table begins:
%e A382364   1 6 = 2 * 3;
%e A382364   2 66 = 2 * 3 * 11;
%e A382364   3 858 = 2 * 3 * 11 * 13;
%e A382364   4 72930 = 2 * 3 * 5 * 11 * 13 * 17;
%e A382364   5 6374082 = 2 * 3 * 11 * 13 * 17 * 19 * 23;
%e A382364   6 643782282 = 2 * 3 * 11 * 13 * 17 * 19 * 23 * 101;
%e A382364   7 66309575046 = 2 * 3 * 11 * 13 * 17 * 19 * 23 * 101 * 103;
%o A382364 (PARI) isok(k, n) = if (issquarefree(k), my(f=factor(k)[,1]); sum(i=1, #f, #digits(f[i])) == n+#digits(k));
%o A382364 a(n) = my(k=2); while (!isok(k, n), k++); k; \\ _Michel Marcus_, Apr 02 2025
%Y A382364 Cf. A055642, A095411.
%K A382364 nonn,base,more
%O A382364 1,1
%A A382364 _Jean-Marc Rebert_, Mar 24 2025