0,1

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

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

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

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

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

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

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.

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.

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 (donovan.johnson(AT)yahoo.com), Aug 31 2008]

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

Cf. A001358, A055394, A066649, A123048.

Sequence in context: A162991 A062926 A069020 this_sequence A041777 A100517 A041597

Adjacent sequences: A122953 A122954 A122955 this_sequence A122957 A122958 A122959

more,nonn

Jonathan Vos Post (jvospost3(AT)gmail.com) & Robert G. Wilson v (rgwv(AT)rgwv.com), Sep 29 2006

a(7) from Donovan Johnson (donovan.johnson(AT)yahoo.com), Aug 31 2008