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Search: id:A119242
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| A119242 |
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Least number k such that there are exactly n powerful numbers between k^2 and (k+1)^2. |
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+0
2
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| 1, 2, 5, 31, 234, 1822, 3611, 17329, 1511067, 524827, 180469424, 472532614
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Pettigrew gives a(1)-a(6) in table 14. He conjectures that k exists for every n. Surprisingly, a(8) is greater than 10^6, but a(9)=524827. The Mathematica program creates all powerful numbers <= nMax by computing all products of the form x^2 y^3.
a(10) is greater than 10^8. - Giovanni Resta (g.resta(AT)iit.cnr.it), May 11 2006
a(n) > 10^9 for n >= 12. [From Donovan Johnson (donovan.johnson(AT)yahoo.com), Dec 07 2008]
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LINKS
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Steve Pettigrew, Sur la distribution de nombres speciaux consecutifs, M.Sc. Thesis, Univ. Laval, 2000.
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EXAMPLE
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a(3)=31 because 968, 972 and 1000 are between 961 and 1024.
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MATHEMATICA
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nMax=10^12; lst={}; Do[lst=Join[lst, i^3 Range[Sqrt[nMax/i^3]]^2], {i, nMax^(1/3)}]; lst=Union[lst]; n=0; k=1; Do[n0=k; While[lst[[k]]<j^2, k++ ]; n1=k; If[n1-n0-1==n, Print[{n, j-1}]; n++ ], {j, Sqrt[nMax]}]
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CROSSREFS
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Sequence in context: A059086 A107389 A077483 this_sequence A068145 A032112 A058009
Adjacent sequences: A119239 A119240 A119241 this_sequence A119243 A119244 A119245
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KEYWORD
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more,nonn
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AUTHOR
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T. D. Noe (noe(AT)sspectra.com), May 09 2006
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EXTENSIONS
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a(8) and the previously known a(9) from Giovanni Resta (g.resta(AT)iit.cnr.it), May 11 2006
a(10)-a(11) from Donovan Johnson (donovan.johnson(AT)yahoo.com), Dec 07 2008
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