A185542 - OEIS

%I #13 Feb 27 2024 19:16:12

%S 1,15,120,528,1540,3916,8385,16471,29646,50086,80601,124251,185745,

%T 269011,379756,524800,709836,944625,1237951,1599366,2041210,2577585,

%U 3216916,3980431,4884375,5939181,7172578,8605026,10253656,12149985,14313925,16776528,19565640,22717170,26263128,30236976,34673628

%N a(n) = m*(m+1)/2, where m = floor(n^(5/2)).

%C A subsequence of A000217, the triangular numbers.

%H G. C. Greubel, <a href="/A185542/b185542.txt">Table of n, a(n) for n = 1..5000</a>

%F a(n) = A000217(A155013(n)). - _Michel Marcus_, Jul 08 2017

%t f[n_] = Floor[n^(5/2)]*Floor[n^(5/2)+1]/2; Table[f[n],{n,1,80}]

%t (#(#+1))/2&/@Floor[Range[40]^(5/2)] (* _Harvey P. Dale_, Feb 27 2024 *)

%o (PARI) for(n=1,50, print1(floor(n^(5/2))*floor(1 + n^(5/2))/2, ", ")) \\ _G. C. Greubel_, Jul 07 2017

%Y Cf. A000217, A155013.

%K nonn

%O 1,2

%A _Clark Kimberling_, Jan 30 2011