%I #16 Sep 19 2020 06:16:07

%S 1,2,6,15,12,25,43,73,480,1981,3205,9038,16099,376340,211318,2461230,

%T 2253517,16907618,106308537,312911063

%N Least number k such that there are exactly n cubefull numbers between k^3 and (k+1)^3.

%C a(n) = least k such that A337736(k) = n.

%C Shiu (1991) proved that infinitely many values of k exist for every n. Therefore, this sequence is infinite.

%H P. Shiu, <a href="https://doi.org/10.1017/S0017089500008351">The distribution of cube-full numbers</a>, Glasgow Mathematical Journal, Vol. 33, No. 3 (1991), pp. 287-295. See section 3, p. 291.

%e a(0) = 1 since there are no cubefull numbers between 1^3 = 1 and 2^3 = 8.

%e a(1) = 2 since there is one cubefull number, 16 = 2^4, between 2^3 = 8 and 3^3 = 27.

%e a(2) = 6 since there are 2 cubefull numbers, 243 = 3^5 and 256 = 2^8, between 6^3 = 216 and 7^3 = 343.

%t cubQ[n_] := Min[FactorInteger[n][[;; , 2]]] > 2; f[n_] := Count[Range[n^3 + 1, (n + 1)^3 - 1], _?cubQ]; mx = 8; s = Table[0,{mx}]; c = 0; n = 1; While[c < mx, i = f[n] + 1; If[i <= mx && s[[i]] == 0, c++; s[[i]] = n]; n++] ;s

%Y Cf. A000578, A036966, A119242, A337736.

%K nonn,more

%O 0,2

%A _Amiram Eldar_, Sep 17 2020

%E a(12)-a(16) from _David A. Corneth_, Sep 18 2020

%E a(17)-a(19) from _Bert Dobbelaere_, Sep 19 2020