

A056781


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


5



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
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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, A035033A035035.
Sequence in context: A115919 A038701 A127072 * A079446 A322546 A283262
Adjacent sequences: A056778 A056779 A056780 * A056782 A056783 A056784


KEYWORD

fini,full,nonn


AUTHOR

Labos Elemer, Aug 18 2000


STATUS

approved



