A323733 - OEIS

%I #7 Jan 27 2019 08:47:31

%S 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,

%T 29,30,31,32,33,34,35,36,37,38,39,40,42,43,44,45,46,47,48,49,51,52,53,

%U 55,56,57,58,59,60,61,62,63,64,65,66,68,69,70,71,72,73

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

%C Complement of A323732.

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

%C Equivalently:

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

%C numbers k such that A323731(k) > 1;

%C numbers k such that A323734(k) > 1.

%e 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.

%e There exists no j > 1 such that j^14 has exactly j divisors, so 14 is not a term.

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

%K nonn

%O 1,3

%A _Jon E. Schoenfield_, Jan 26 2019