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A056781
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Prime powers such that the 4th power of the number of divisors is not smaller than the number itself.
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4
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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; internal format)
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OFFSET
| 1,1
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COMMENTS
| For any integers n, d[n]^4>n should form finite albeit very large sequence.
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FORMULA
| p^w<=(w+1)^4 i.e. p<=(w+1)^(4/w) restricts possible primes and their exponents
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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
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CROSSREFS
| A000005, A034884, A035033-A035035.
Sequence in context: A115919 A038701 A127072 * A079446 A115975 A087797
Adjacent sequences: A056778 A056779 A056780 * A056782 A056783 A056784
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KEYWORD
| fini,full,nonn
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AUTHOR
| Labos E. (labos(AT)ana.sote.hu), Aug 18 2000
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