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%I #7 Jul 15 2017 11:05:24
%S 2,3,4,5,7,8,9,11,13,16,25,27,32,49,64,81,125,128,243,256,512,625,729,
%T 1024,2048,2187,4096,6561,8192,16384,32768,65536
%N Prime powers such that the 4th power of the number of divisors is not smaller than the number itself.
%C For any integers n, d[n]^4>n should form finite albeit very large sequence.
%F p^w<=(w+1)^4 i.e. p<=(w+1)^(4/w) restricts possible primes and their exponents
%e Equality holds in 12 cases: n=6561=3^8,d[n]=9 and d^4=9^4=3^8=n n=625,d[n]=5, so d^4=n
%t Select[Select[Range[2^16], PrimePowerQ], DivisorSigma[0, #]^4 >= # &] (* _Michael De Vlieger_, Jul 15 2017 *)
%Y A000005, A034884, A035033-A035035.
%K fini,full,nonn
%O 1,1
%A _Labos Elemer_, Aug 18 2000
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