A373348 Squarefree numbers k such that there exists a k-digit multiple of k that has k divisors.

1, 11, 206, 500015

Offset: 1

Author

Jon E. Schoenfield, Jun 01 2024

Keywords

• nonn
• more

Comments

Squarefree numbers k such that A182749(k) and A182750(k) are nonzero.

a(2) = 11 is the only prime term.

Conjecture: a(3) = 206 = 2*103 and a(4) = 500015 = 5*100003 are the only semiprime terms.

Examples

			The table below lists the known terms k and, for each k, the corresponding multiple:
.
  n   a(n) = k   k-digit multiple of k having k divisors
  -   --------   -----------------------------------------
  1          1   1
  2         11   11^10 = 25937424601
  3        206   2 * 103^102 = 4.0778...*10^205
  4     500015   5^4 * 100003^100002 = 1.2553...*10^500014
		

Crossrefs

Cf. A182749, A182750.