A228432 Sum_{i=1..floor(prime(n)/4)} floor(sqrt(i*prime(n))).

0, 0, 2, 2, 7, 14, 24, 25, 37, 70, 71, 114, 140, 143, 170, 234, 274, 310, 357, 399, 444, 498, 552, 660, 784, 850, 856, 926, 990, 1064, 1310, 1395, 1564, 1574, 1850, 1859, 2054, 2173, 2277, 2494, 2623, 2730, 2986, 3104, 3234, 3246, 3656, 4085, 4235, 4370

Offset: 1

Author

Michel Marcus, Nov 11 2013

Keywords

• nonn

Comments

If p = prime(n) in A002145 and n>3, or said differently, if n in A080148 and n>1, then a(n) = A081115(n).

Examples

			For n=7, p=17 and a(7) = floor(sqrt(17)) + floor(sqrt(34)) + floor(sqrt(51)) + floor(sqrt(68)) = 4+5+7+8 = 24.
		

Links

• S. A. Shirali, A family portrait of primes -- a case study in discrimination, Math. Mag., Vol. 70, No. 4 (Oct. 1997), pp. 263-272.

Crossrefs

Cf. A002145, A080148, A081115.

Programs

Mathematica

Table[p = Prime[n]; Sum[Floor[Sqrt[i*p]], {i, Floor[p/4]}], {n, 100}] (* T. D. Noe, Nov 13 2013 *)

PARI

a(n) = p = prime(n); sum(i=1, p\4, sqrtint(i*p));