A172433 Let u(n) = Sum [n/[sqrt k]] and v(n) = Sum [n/(sqrt k)] where the summation index k ranges from 1 to infinity, although both sums are actually finite. Here [a] denotes the integer part of a. Then a(n) = u(n) - v(n).

2, 6, 9, 16, 17, 27, 26, 36, 38, 48, 43, 67, 59, 67, 72, 88, 75, 102, 86, 111, 115, 123, 99, 150, 137, 142, 139, 169, 141, 192, 166, 192, 186, 189, 176, 253, 214, 217, 207, 263, 223, 284, 239, 269, 285, 285, 230, 332, 294, 325, 305, 339, 282, 350, 324, 391, 370, 369, 300, 448, 382, 377, 385, 438, 400

Offset: 1

Author

Ali A. Tanara (aatanara(AT)gmail.com), Feb 02 2010

Keywords

• nonn

Comments

One can pick out the values of the sequence at primes, obtaining the new sequence 6,9,17,26,43,59,75,86,99,141 which seems to be monotone, unlike the original sequence.

Actually, the infinite sum can be replaced by a finite sum with terms up to (n+1)^2 (see second PARI script). Apparently v(n) is A153818(n). - Michel Marcus, Jul 17 2013

Programs

PARI

a(n) = round(suminf(k=1, floor(n/sqrtint(k))) - suminf(k=1, floor(n/sqrt(k)))) \\ Michel Marcus, Jul 17 2013

PARI

a(n) = sum(k=1, (n+1)^2, floor(n/sqrtint(k))) - sum(k=1, (n+1)^2, floor(n/sqrt(k))) \\ Michel Marcus, Jul 17 2013

Extensions

Definition clarified by Gihan Marasingha (G_Marasingha(AT)hotmail.com), Feb 10 2010