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 A137319 Start with the set of natural numbers. Add 1 to every 2nd term, 2 to every 3rd term, 3 to every 4th term, etc. 11
 1, 3, 5, 8, 9, 14, 13, 19, 19, 24, 21, 34, 25, 34, 35, 42, 33, 51, 37, 56, 49, 54, 45, 76, 53, 64, 63, 78, 57, 94, 61, 89, 77, 84, 79, 118, 73, 94, 91, 122, 81, 130, 85, 122, 117, 114, 93, 162, 103, 137, 119, 144, 105, 166, 123, 168, 133, 144, 117, 216, 121, 154, 161, 184 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS The generating function is the sum of the generating functions in A000027 and A065608. - R. J. Mathar, Apr 09 2008 LINKS FORMULA a(n) = n + A065608(n). - R. J. Mathar, Apr 09 2008 a(n) = Sum_{k=1..n} k^(1-ceiling(n/k)+floor(n/k)). - Wesley Ivan Hurt, May 24 2021 EXAMPLE Start with the natural numbers:    1,  2,  3,  4,  5,  6,  7,  8,  9, 10, ... add 1 to every 2nd term:    1,  3,  3,  5,  5,  7,  7,  9,  9, 11, ... add 2 to every 3rd term:    1,  3,  5,  5,  5,  9,  7,  9, 11, 11, ... add 3 to every 4th term:    1,  3,  5,  8,  5,  9,  7, 12, 11, 11, ... add 4 to every 5th term:    1,  3,  5,  8,  9,  9,  7, 12, 11, 15, ... etc. MAPLE A137319 := proc(n) local a, k ; a := n ; for k from 2 to n do if n mod k = 0 then a := a+k-1 ; fi ; od: a; end: seq(A137319(n), n=1..100) ; # R. J. Mathar, Apr 09 2008 MATHEMATICA Table[DivisorSigma[1, n] - DivisorSigma[0, n] + n, {n, 100}] (* Vincenzo Librandi, Sep 21 2015 *) CROSSREFS Sequence in context: A186621 A002159 A050094 * A138808 A185456 A308405 Adjacent sequences:  A137316 A137317 A137318 * A137320 A137321 A137322 KEYWORD easy,nonn AUTHOR Ctibor O. Zizka, Apr 06 2008 EXTENSIONS Corrected and extended by R. J. Mathar, Apr 09 2008 Edited by Jon E. Schoenfield, Sep 21 2015 STATUS approved

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Last modified May 28 08:23 EDT 2022. Contains 354112 sequences. (Running on oeis4.)