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

1,1

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, ...

Links

Table of n, a(n) for n=1..24.

Example

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.

Sequence in context: A167201 A336145 A269871 * A048769 A190514 A085950

Adjacent sequences: A323729 A323730 A323731 * A323733 A323734 A323735

Keyword

nonn,more

Author

Jon E. Schoenfield, Jan 26 2019

Status

approved