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%I #7 Jul 26 2024 16:13:32
%S 1,11,206,500015
%N Squarefree numbers k such that there exists a k-digit multiple of k that has k divisors.
%C Squarefree numbers k such that A182749(k) and A182750(k) are nonzero.
%C a(2) = 11 is the only prime term.
%C Conjecture: a(3) = 206 = 2*103 and a(4) = 500015 = 5*100003 are the only semiprime terms.
%e The table below lists the known terms k and, for each k, the corresponding multiple:
%e .
%e n a(n) = k k-digit multiple of k having k divisors
%e - -------- -----------------------------------------
%e 1 1 1
%e 2 11 11^10 = 25937424601
%e 3 206 2 * 103^102 = 4.0778...*10^205
%e 4 500015 5^4 * 100003^100002 = 1.2553...*10^500014
%Y Cf. A182749, A182750.
%K nonn,more
%O 1,2
%A _Jon E. Schoenfield_, Jun 01 2024