This site is supported by donations to The OEIS Foundation.

 Annual appeal: Please make a donation to keep the OEIS running! Over 6000 articles have referenced us, often saying "we discovered this result with the help of the OEIS". Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A051336 Number of arithmetic progressions in {1,2,3,...,n}, including trivial arithmetic progressions of lengths 1 and 2. 4
 1, 3, 7, 13, 22, 33, 48, 65, 86, 110, 138, 168, 204, 242, 284, 330, 381, 434, 493, 554, 621, 692, 767, 844, 929, 1017, 1109, 1205, 1307, 1411, 1523, 1637, 1757, 1881, 2009, 2141, 2282, 2425, 2572, 2723, 2882, 3043, 3212, 3383, 3560, 3743, 3930, 4119 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS T. D. Noe, Table of n, a(n) for n=1..1000 FORMULA Theorem: the second differences give tau(n+1), the number of divisors of n+1 (A000005). The number of arithmetic subsequences of [1, ..., n] with successive-term increment i and length k is (n-i*(k-1))(i > 0, k > 0, n > i*(k-1)). - Robert E. Sawyer (rs.1(AT)mindspring.com) a(n) = n + sum { i=1..n-1, j=1..floor(n/i) } (n - i*j). - Robert E. Sawyer (rs.1(AT)mindspring.com) EXAMPLE a(1): [1]; a(2): [1],[2],[1,2]; a(3): [1],[2],[3],[1,2],[1,3],[2,3],[1,2,3]. MATHEMATICA nmax = 48; t = Table[ DivisorSigma[0, n], {n, 1, nmax}]; Accumulate[ Accumulate[t]+1] - Accumulate[t] (* Jean-François Alcover, Nov 08 2011 *) With[{c=Accumulate[DivisorSigma[0, Range[50]]]}, Accumulate[c+1]-c] (* Harvey P. Dale, Dec 23 2015 *) CROSSREFS a(n) = n + A078567(n). Cf. A000005, A054519. Sequence in context: A155354 A136219 A078582 * A253896 A002623 A173196 Adjacent sequences:  A051333 A051334 A051335 * A051337 A051338 A051339 KEYWORD nonn,easy,nice AUTHOR John W. Layman, Nov 02 1999 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.