cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

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%I A323733 #7 Jan 27 2019 08:47:31
%S A323733 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 A323733 29,30,31,32,33,34,35,36,37,38,39,40,42,43,44,45,46,47,48,49,51,52,53,
%U A323733 55,56,57,58,59,60,61,62,63,64,65,66,68,69,70,71,72,73
%N A323733 Numbers k for which there exists at least one number j > 1 such that j^k has exactly j divisors.
%C A323733 Complement of A323732.
%C A323733 This sequence lists the numbers k such that A073049(k) > 0.
%C A323733 Equivalently:
%C A323733 numbers k for which 1 is not the only number j such that j^k has exactly j divisors;
%C A323733 numbers k such that A323731(k) > 1;
%C A323733 numbers k such that A323734(k) > 1.
%e A323733 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 A323733 There exists no j > 1 such that j^14 has exactly j divisors, so 14 is not a term.
%Y A323733 Cf. A000005, A073049, A323730, A323731, A323732, A323734.
%K A323733 nonn
%O A323733 1,3
%A A323733 _Jon E. Schoenfield_, Jan 26 2019