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%I #10 Jan 27 2019 08:47:22
%S 5,14,21,41,50,54,67,76,86,90,111,113,119,131,142,153,165,175,186,202,
%T 204,216,224,230
%N Numbers k for which there exists no j > 1 such that j^k has exactly j divisors.
%C This sequence lists the numbers k such that A073049(k) = 0.
%C Equivalently:
%C numbers k for which the only number j such that j^k has exactly j divisors is 1;
%C numbers k such that A323731(k)=1;
%C numbers k such that A323734(k)=1.
%C The complement of this sequence is A323733.
%C 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, ...
%e There exists no j > 1 such that j^5 has exactly j divisors, so 5 is a term.
%e 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.
%Y Cf. A000005, A073049, A323730, A323731, A323733, A323734.
%K nonn,more
%O 1,1
%A _Jon E. Schoenfield_, Jan 26 2019