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

1,1

Comments

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

Links

Table of n, a(n) for n=1..32.

Formula

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

Example

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

Mathematica

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

Crossrefs

A000005, A034884, A035033-A035035.

Sequence in context: A038701 A127072 A341089 * A079446 A322546 A283262

Adjacent sequences: A056778 A056779 A056780 * A056782 A056783 A056784

Keyword

fini,full,nonn

Author

Labos Elemer, Aug 18 2000

Status

approved