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Search: id:A036454
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| A036454 |
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Prime powers with special exponents: q^(p-1) where both p and q are arbitrary prime numbers. |
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+0
5
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| 4, 9, 16, 25, 49, 64, 81, 121, 169, 289, 361, 529, 625, 729, 841, 961, 1024, 1369, 1681, 1849, 2209, 2401, 2809, 3481, 3721, 4096, 4489, 5041, 5329, 6241, 6889, 7921, 9409, 10201, 10609, 11449, 11881, 12769, 14641, 15625, 16129, 17161, 18769, 19321
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Composite numbers with a prime number of divisors.
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..1000
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FORMULA
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Nest[ d, a[ n ], 2 ]=2 or d[ d[ a[ n ] ] ]=2, where d[ x ]=tau[ x ]=sigma[ 0, x ], the number of divisors of x.
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EXAMPLE
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From powers of 2 4,16,64,1024,4096,65536 are in the sequence since exponent+1 is also prime. The same powers of any prime base also included.. d[ a[ n ] ]=p-1+1=p and d[ d[ [ a[ n ] ] ]=2 already stationary.
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PROGRAM
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(PARI) for(n=1, 34000, if(isprime(n), n++, x=numdiv(n); if(isprime(x), print(n))))
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CROSSREFS
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Cf. A000005, A036450, A036452, A010553.
Cf. A009087
Sequence in context: A075494 A063735 A056798 this_sequence A115648 A082522 A133900
Adjacent sequences: A036451 A036452 A036453 this_sequence A036455 A036456 A036457
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KEYWORD
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nonn,easy,nice
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AUTHOR
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Labos E. (labos(AT)ana.sote.hu)
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