A069553 Define S(k) to be the sequence of divisors and multiples of k, e.g. S(1) = 1,2,3,4,5... S(2) = 1,2,4,6,8,10,... S(10) = 1,2,5,10,20,30,40,50,...; a(n) = n-th term of the n-th sequence S(n).

1, 2, 6, 8, 20, 18, 42, 40, 63, 70, 110, 84, 156, 154, 180, 192, 272, 234, 342, 300, 378, 418, 506, 408, 575, 598, 648, 644, 812, 690, 930, 864, 990, 1054, 1120, 1008, 1332, 1330, 1404, 1320, 1640, 1470, 1806, 1716, 1800, 1978, 2162, 1872, 2303, 2250, 2448

Offset

1,2

Links

Ivan Neretin, Table of n, a(n) for n = 1..10000

Formula

a(n) = n*{n - d(n) + 1} where d(n) = number of divisors of n.

Mathematica

Table[n (n + 1 - DivisorSigma[0, n]), {n, 1, 51}] (* Ivan Neretin, May 25 2015 *)

Prog

(PARI) a(n) =  n*(n - numdiv(n) + 1); \\ Michel Marcus, Sep 17 2013

Crossrefs

Sequence in context: A140965 A002618 A135616 * A275826 A371238 A143481

Adjacent sequences: A069550 A069551 A069552 * A069554 A069555 A069556

Keyword

nonn

Author

Amarnath Murthy, Mar 22 2002

Extensions

Corrected and extended by Ray Chandler, Sep 29 2003

Status

approved