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

1,1

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

Links

Table of n, a(n) for n=1..65.

Prog

(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

Crossrefs

Sequence in context: A355738 A329743 A320496 * A049622 A043548 A347535

Adjacent sequences: A172430 A172431 A172432 * A172434 A172435 A172436

Keyword

nonn

Author

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

Extensions

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

Status

approved