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Search: id:A061236
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| A061236 |
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Smallest number with p(n)^3 divisors where p(n) is n-th prime. |
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+0
1
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| 24, 900, 810000, 729000000, 590490000000000, 531441000000000000, 430467210000000000000000, 387420489000000000000000000, 313810596090000000000000000000000
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OFFSET
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1,1
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FORMULA
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For p=2, 24 is the solution. If p>2 prime, then suitable powers of 30 are the least solutions: a(n)=Min{x|d(x)=A000005(x)=p(n)^3}=30^[p(n)-1], p(n)=nth prime; d[2^(ppp-1)]=d[2^(pp-1)3^(p-1)]=d[30^(p-1)]=p^3, and 2^(ppp-1)>2^(pp-1)3^(p-1)>30^(p-1) holds if p>2.
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EXAMPLE
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p=2, then d(128)=d(24)=d(30)=8 and a(1)=24<30 is the smallest; P=5, then 2^124>(2^24)*(3^4)>30^4=810000=a(3).
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CROSSREFS
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Cf. A000005, A005179, A003680, A037992, A061283, A061286, A061148, A061149.
Sequence in context: A109575 A107391 A006147 this_sequence A001784 A001866 A033590
Adjacent sequences: A061233 A061234 A061235 this_sequence A061237 A061238 A061239
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KEYWORD
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nonn
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AUTHOR
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Labos E. (labos(AT)ana.sote.hu), Jun 01 2001
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