A323732 Numbers k for which there exists no j > 1 such that j^k has exactly j divisors.

5, 14, 21, 41, 50, 54, 67, 76, 86, 90, 111, 113, 119, 131, 142, 153, 165, 175, 186, 202, 204, 216, 224, 230

Offset: 1

Author

Jon E. Schoenfield, Jan 26 2019

Keywords

• nonn
• more

Comments

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

Equivalently:

numbers k for which the only number j such that j^k has exactly j divisors is 1;

numbers k such that A323731(k)=1;

numbers k such that A323734(k)=1.

The complement of this sequence is A323733.

The next terms after a(24)=230 appear to be 233, 253, 269, 273, 285, 293, 303, 307, 318, 321, 328, 345, 354, 357, 369, 370, 373, 384, 393, 402, 410, 412, 414, 426, 429, 431, 440, 441, 445, 468, ...

Examples

			There exists no j > 1 such that j^5 has exactly j divisors, so 5 is a term.
For k=15 and j=976, j^k = 976^15 = (2^4 * 61)^15 = 2^60 * 61^15, which has exactly (60+1)*(15+1) = 61*16 = 976 = j divisors, so k=15 is not a term.
		

Crossrefs

Cf. A000005, A073049, A323730, A323731, A323733, A323734.