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.

6, 66, 858, 72930, 6374082, 643782282, 66309575046

Offset: 1

Author

Jean-Marc Rebert, Mar 24 2025

Keywords

• nonn
• base
• more

Examples

			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.
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.
Table begins:
  1 6 = 2 * 3;
  2 66 = 2 * 3 * 11;
  3 858 = 2 * 3 * 11 * 13;
  4 72930 = 2 * 3 * 5 * 11 * 13 * 17;
  5 6374082 = 2 * 3 * 11 * 13 * 17 * 19 * 23;
  6 643782282 = 2 * 3 * 11 * 13 * 17 * 19 * 23 * 101;
  7 66309575046 = 2 * 3 * 11 * 13 * 17 * 19 * 23 * 101 * 103;
		

Crossrefs

Cf. A055642, A095411.

Programs

PARI

isok(k, n) = if (issquarefree(k), my(f=factor(k)[,1]); sum(i=1, #f, #digits(f[i])) == n+#digits(k));
a(n) = my(k=2); while (!isok(k, n), k++); k; \\ Michel Marcus, Apr 02 2025