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 A119242 Least number k such that there are exactly n powerful numbers between k^2 and (k+1)^2. 2
 1, 2, 5, 31, 234, 1822, 3611, 17329, 1511067, 524827, 180469424, 472532614, 78102676912 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS 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, May 11 2006 a(n) > 10^11 for n >= 13. - Donovan Johnson, Sep 03 2013 LINKS Donovan Johnson, Powerful numbers between k^2 and (k+1)^2 Steve Pettigrew, Sur la distribution de nombres speciaux consecutifs, M.Sc. Thesis, Univ. Laval, 2000. EXAMPLE a(3)=31 because 968, 972 and 1000 are between 961 and 1024. MATHEMATICA 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]]

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Last modified July 5 03:37 EDT 2020. Contains 335459 sequences. (Running on oeis4.)