A238280 Irregular triangle read by rows, T(n,k) = Sum_{i = 1..n} k mod i, k = 1..m where m = lcm(1..n).

0, 1, 0, 2, 2, 1, 1, 3, 0, 3, 4, 4, 1, 4, 2, 5, 2, 2, 3, 6, 0, 4, 6, 7, 5, 4, 3, 7, 5, 6, 3, 7, 2, 6, 8, 4, 2, 6, 5, 9, 2, 3, 5, 9, 4, 3, 5, 6, 4, 8, 2, 6, 4, 5, 7, 6, 1, 5, 7, 8, 1, 5, 4, 8, 6, 2, 4, 8, 3, 7, 4, 5, 3, 7, 6, 5, 3, 4, 6, 10, 0, 5, 8, 10, 9, 9, 3, 8, 7, 9, 7, 12, 2, 7, 10, 7, 6, 11, 5, 10, 4, 6, 9, 14, 4, 4, 7, 9, 8, 13, 2, 7, 6, 8, 11

Offset

1,4

Comments

Row n contains A003418(n) terms.

The penultimate term (the one before zero) of row n = A000217(n-1).

Links

Antti Karttunen, Rows 1..10 of the table, flattened

Kival Ngaokrajang, Illustration for n = 1..10

Example

Row n of this irregular triangle is obtained by taking the first A003418(n) = lcm(1..n) terms (up to and including the first zero) of the following array (which starts at row n=1 and column k=1 and is periodic in each row):
  0; 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0
  1  0; 1  0  1  0  1  0  1  0  1  0  1  0  1  0  1  0  1  0
  2  2  1  1  3  0; 2  2  1  1  3  0  2  2  1  1  3  0  2  2 # A110269
  3  4  4  1  4  2  5  2  2  3  6  0; 3  4  4  1  4  2  5  2
  4  6  7  5  4  3  7  5  6  3  7  2  6  8  4  2  6  5  9  2
  5  8 10  9  9  3  8  7  9  7 12  2  7 10  7  6 11  5 10  4
  6 10 13 13 14  9  8  8 11 10 16  7 13 10  8  8 14  9 15 10
  7 12 16 17 19 15 15  8 12 12 19 11 18 16 15  8 15 11 18 14
  8 14 19 21 24 21 22 16 12 13 21 14 22 21 21 15 23 11 19 16
  9 16 22 25 29 27 29 24 21 13 22 16 25 25 26 21 30 19 28 16

Prog

(Small Basic)
For n = 1 to 20
  k = 1
  loop:
  rs = 0
  For i = 1 To n
    rs = rs + math.Remainder(k, i)
  EndFor
  TextWindow.Write(rs+", ")
  If rs > 0 then
    k = k + 1
    Goto loop
  EndIf
EndFor
(Scheme)
(define (A238280 n) (A238280tabf (A236857 n) (A236858 n)))
(define (A238280tabf n k) (add (lambda (i) (modulo k i)) 1 n))
;; Implements sum_{i=lowlim..uplim} intfun(i):
(define (add intfun lowlim uplim) (let sumloop ((i lowlim) (res 0)) (cond ((> i uplim) res) (else (sumloop (1+ i) (+ res (intfun i)))))))
;; Antti Karttunen, Feb 27 2014

Crossrefs

Cf. A000217, A003418, A173185, A236856, A236857, A236858.

Sequence in context: A235342 A079692 A110269 * A326644 A120964 A318810

Adjacent sequences: A238277 A238278 A238279 * A238281 A238282 A238283

Keyword

nonn,tabf

Author

Kival Ngaokrajang, Feb 22 2014

Status

approved