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%I #19 Nov 07 2023 11:17:52
%S 1,625,6561,4100625
%N Positive integers k such that the fourth power of the number of positive divisors of k equals k.
%C 625=5^4, 6561=3^8, 4100625=(3^8)(5^4).
%C There are no more terms in the sequence.
%D T. Andreescu, D. Andrica and Z. Feng, 104 Number Theory Problems (from the training of the USA IMO team), Birkhäuser, Boston, 2007, Advanced problem # 19, pp. 85, 145, 146.
%D Roozbeh Hazrat, Mathematica: A Problem-Centered Approach, Springer 2010, p. 39.
%e 625 has 5 divisors (1, 5, 25, 125 and 625) and 5^4 = 625.
%t Select[Range[4200000],DivisorSigma[0,#]^4==#&] (* _Harvey P. Dale_, Oct 17 2011 *)
%Y Cf. A066693, A180936.
%K fini,nonn,full
%O 1,2
%A _Emeric Deutsch_, Aug 11 2008
%E Second reference added by _Harvey P. Dale_, Oct 17 2011
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