A056781 Prime powers such that the 4th power of the number of divisors is not smaller than the number itself.

2, 3, 4, 5, 7, 8, 9, 11, 13, 16, 25, 27, 32, 49, 64, 81, 125, 128, 243, 256, 512, 625, 729, 1024, 2048, 2187, 4096, 6561, 8192, 16384, 32768, 65536

Offset: 1

Author

Labos Elemer, Aug 18 2000

Keywords

• fini
• full
• nonn

Comments

For any integers n, d[n]^4>n should form finite albeit very large sequence.

Examples

			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
		

Crossrefs

A000005, A034884, A035033-A035035.

Programs

Mathematica

Select[Select[Range[2^16], PrimePowerQ], DivisorSigma[0, #]^4 >= # &] (* Michael De Vlieger, Jul 15 2017 *)

Formula

p^w<=(w+1)^4 i.e. p<=(w+1)^(4/w) restricts possible primes and their exponents