A122956 - OEIS

%I #6 Mar 30 2012 18:40:38

%S 4,9,65,11665,27289,3030569,6808609,1632201497,10553247449,

%T 843404126561,2101614761177,62537392166201,100301302204489

%N Least semiprime composed of a square and a positive cube in n different ways.

%C a(n) for n>0 must be odd.

%e a(0)=4 since it is the first semiprime (2*2) not of the form a^2+b^3.

%e a(1) = 9 = 1^2 + 2^3 = 3*3.

%e a(2) = 65 = 1^2 + 4^3 = 8^2 + 1^3 = 5*13.

%e a(3) = 11665 = 108^2 + 1^3 = 107^2 + 6^3 = 87^2 + 16^3 = 5*2333.

%e a(4) = 27289 = 165^2 + 4^3 = 129^2 + 22^3 = 108^2 + 25^2 = 17^2 + 30^3 = 29*941.

%e a(5) = 3030569 = 1671^2 + 62^3 = 1587^2 + 80^3 = 1038^2 + 125^3 = 913^2 + 130^3 = 409^2 + 142^3 = 103*29423.

%e a(6) = 6808609 = 2609^2 + 12^3 = 2445^2 + 94^3 = 1853^2 + 150^3 = 1647^2 + 160^3 = 1522^2 + 165^3 = 1124^2 + 177^3 = 103*66103.

%e a(7) = 1632201497 = 38425^2 + 538^3 = 38202^2 + 557^3 = 36741^2 + 656^3 = 26177^2 + 982^3 = 18555^2 + 1088^3 = 13477^2 + 1132^3 = 1292^2 + 1177^3. [From _Donovan Johnson_, Aug 31 2008]

%e Contribution from _Donovan Johnson_, Mar 01 2010: (Start)

%e a(8) = 10553247449 = 102729^2 + 2^3 = 102393^2 + 410^3 = 101551^2 + 622^3 = 101371^2 + 652^3 = 80357^2 + 1600^3 = 63768^2 + 1865^3 = 13893^2 + 2180^3 = 4581^2 + 2192^3.

%e a(9) = 843404126561 = 917123^2 + 1318^3 = 902037^2 + 3098^3 = 866353^2 + 4528^3 = 833585^2 + 5296^3 = 634581^2 + 7610^3 = 521169^2 + 8300^3 = 478831^2 + 8500^3 = 259331^2 + 9190^3 = 23805^2 + 9446^3.

%e a(10) = 2101614761177 = 1449189^2 + 1136^3 = 1448961^2 + 1286^3 = 1448167^2 + 1642^3 = 1421577^2 + 4322^3 = 1315794^2 + 7181^3 = 1271813^2 + 7852^3 = 1119559^2 + 9466^3 = 1085568^2 + 9737^3 = 668475^2 + 11828^3 = 438431^2 + 12406^3.

%e a(11) = 62537392166201 = 7908053^2 + 448^3 = 7906101^2 + 3140^3 = 7863087^2 + 8918^3 = 7778399^2 + 12670^3 = 7537351^2 + 17890^3 = 7205845^2 + 21976^3 = 6649899^2 + 26360^3 = 5818649^2 + 30610^3 = 5684351^2 + 31150^3 = 2900985^2 + 37826^3 = 1009845^2 + 39476^3.

%e a(12) = 100301302204489 = 10013433^2 + 3190^3 = 9966435^2 + 9904^3 = 9922058^2 + 12285^3 = 9879183^2 + 13930^3 = 9821564^2 + 15657^3 = 9740881^2 + 17562^3 = 7540415^2 + 35154^3 = 2704995^2 + 45304^3 = 2667144^2 + 45337^3 = 1300067^2 + 46200^3 = 614915^2 + 46404^3 = 54519^2 + 46462^3.

%e (End)

%t semiPrimeQ[x_] := Plus @@ Last /@ FactorInteger@x == 2; t = Table[0, {10}]; Do[ If[ semiPrimeQ@n, c = Count[IntegerQ /@ Sqrt[n - Range@Floor[n^(1/3)]^3], True]; If[ t[[c + 1]] == 0, t[[c + 1]] = n; Print[{c, n}] ]], {n, 731000000}]; t

%Y Cf. A001358, A055394, A066649, A123048.

%K more,nonn

%O 0,1

%A _Jonathan Vos Post_ & _Robert G. Wilson v_, Sep 29 2006

%E a(7) from _Donovan Johnson_, Aug 31 2008

%E a(8)-a(12) from _Donovan Johnson_, Mar 01 2010