The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS For any integers n, d[n]^4>n should form finite albeit very large sequence. LINKS 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 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified May 17 08:48 EDT 2021. Contains 343966 sequences. (Running on oeis4.)