A319022 a(n) is the smallest number with n distinct prime factors whose decimal representation contains all its prime factors, taking multiplicity into account.

2, 119911, 2510, 21372, 1943795, 73171842, 113678565, 13121675970, 297115923720, 73605381139290, 255360234137190, 43759729761726090

Offset

1,1

Comments

A version of A318965.

If a term t is divisible by a prime power p^k, then p must appear at least k times in the decimal representation of t. The copies of p are allowed to overlap; however, in the first 12 terms of the sequence, this does not occur, and only a(2), a(4), and a(9) are nonsquarefree.

a(n) >= A318965(n) by definition. If A318965(n) is squarefree, then a(n) = A318965(n). But a(n) = A318965(n) can also hold for a(n) that is nonsquarefree; e.g., a(4) = A318965(4).

Links

Table of n, a(n) for n=1..12.

Example

a(2) = 119911 = 11 * 11 * 991.
a(3) = 2510 = 2 * 5 * 251.
a(4) = 21372 = 2 * 2 * 3 * 13 * 137.
a(5) = 1943795 = 5 * 7 * 19 * 37 * 79.
a(6) = 73171842 = 2 * 3 * 17 * 31 * 73 * 317.
a(7) = 113678565 = 3 * 5 * 7 * 11 * 13 * 67 * 113.

Crossrefs

Cf. A083359, A131930, A318965.

Sequence in context: A231612 A296104 A170995 * A003840 A122540 A324438

Adjacent sequences: A319019 A319020 A319021 * A319023 A319024 A319025

Keyword

nonn,base,more

Author

Altug Alkan, Sep 08 2018

Extensions

Terms computed by Giovanni Resta, Sep 08 2018

Status

approved