A182750 -id:A182750 - cp's OEIS frontend

A182749 a(n) = the smallest multiple of n with n digits and exactly n divisors. a(n) = 0 if no such number exists.

1, 0, 0, 0, 0, 0, 0, 10000024, 100580841, 0, 25937424601, 100000000068, 0, 0, 0, 1000000000001152, 0, 100000000000000404, 0, 10000000000000000880, 0, 0, 0, 100000000000000000001184, 1000060001350013500050625, 0, 100000000015460000000597529, 1000000000000000000000022464

Offset: 1

Jaroslav Krizek, Nov 27 2010

Conjecture: a(n) > 0 for all nonsquarefree n except for n = 4. - Jon E. Schoenfield, Jun 01 2024

Jon E. Schoenfield, Table of n, a(n) for n = 1..100

Cf. A000005, A073904, A182750.

A000005(a(n)) = n for a(n) > 0.

a(n) <= A182750(n).

a(16), a(18), a(20) corrected by Jon E. Schoenfield, May 26 2024
a(21)-a(23) (implied by A182750) from Pontus von Brömssen, May 26 2024
a(24)-a(25) from Michael S. Branicky, May 26 2024
a(26)-a(28) from Jon E. Schoenfield, May 26 2024

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

Original entry on oeis.org

1, 11, 206, 500015

Offset: 1

Jon E. Schoenfield, Jun 01 2024

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.

			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

Cf. A182749, A182750.

cp's OEIS Frontend

A182749 a(n) = the smallest multiple of n with n digits and exactly n divisors. a(n) = 0 if no such number exists.

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