OFFSET
1,2
COMMENTS
The terms with an odd number of digits are squares.
The terms with 2 digits are squarefree semiprimes (cf. A006881) Union {27}. The terms with 3 digits belong to A030627 (numbers with 9 divisors) and the ones with 4 digits belong to A030634 (numbers with 16 divisors).
The number of terms b(n) with n digits begins with: 1, 30, 7, 753, 3, 11409, 2, ... When there are an odd number of digits, the number of terms decreases from b(3) = 7, b(5) = 3, b(7) = 2. Is there a 2q+1 such that b(2q+1) = 0?
The sequence is infinite because 10^k is the term for each k. We have tau(10^k) = tau(2^k)*tau(5^k) = (k + 1)^2 and 10^k has k + 1 digits. - Marius A. Burtea, May 09 2019
a(n) >= 1, for any n, so b(2q+1)>= 1 for any q. - Marius A. Burtea, May 09 2019
LINKS
Sean A. Irvine, Java program (github)
EXAMPLE
65 is a term with 2 digits and 4 divisors: {1, 5, 13, 65}.
484 is a term with 3 digits and 9 divisors: {1, 2, 4, 11, 22, 44, 121, 242, 484}.
PROG
(PARI) is(n) = numdiv(n) == #digits(n)^2 \\ David A. Corneth, May 08 2019
(Magma) [n:n in [1..1500]|NumberOfDivisors(n) eq (#Intseq(n))^2]; // Marius A. Burtea, May 09 2019
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Bernard Schott, May 08 2019
STATUS
approved