A323733 Numbers k for which there exists at least one number j > 1 such that j^k has exactly j divisors.

0, 1, 2, 3, 4, 6, 7, 8, 9, 10, 11, 12, 13, 15, 16, 17, 18, 19, 20, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 42, 43, 44, 45, 46, 47, 48, 49, 51, 52, 53, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 68, 69, 70, 71, 72, 73

Offset

1,3

Comments

Complement of A323732.

This sequence lists the numbers k such that A073049(k) > 0.

Equivalently:

numbers k for which 1 is not the only number j such that j^k has exactly j divisors;

numbers k such that A323731(k) > 1;

numbers k such that A323734(k) > 1.

Links

Table of n, a(n) for n=1..67.

Example

For k=9 and j=640, j^k = 640^9 = (2^7 * 5)^9 = 2^63 * 5^9, which has exactly (63+1)*(9+1) = 64*10 = 640 = j divisors, so k=9 is a term.
There exists no j > 1 such that j^14 has exactly j divisors, so 14 is not a term.

Crossrefs

Cf. A000005, A073049, A323730, A323731, A323732, A323734.

Sequence in context: A276389 A302058 A183302 * A003247 A076216 A013919

Adjacent sequences: A323730 A323731 A323732 * A323734 A323735 A323736

Keyword

nonn

Author

Jon E. Schoenfield, Jan 26 2019

Status

approved