A173185 -id:A173185 - cp's OEIS frontend

A236856 Partial sums of A003418 starting summing from A003418(1), with a(0) = 0.

0, 1, 3, 9, 21, 81, 141, 561, 1401, 3921, 6441, 34161, 61881, 422241, 782601, 1142961, 1863681, 14115921, 26368161, 259160721, 491953281, 724745841, 957538401, 6311767281, 11665996161, 38437140561, 65208284961, 145521718161, 225835151361, 2554924714161

Offset: 0

Antti Karttunen, Feb 27 2014

nonn

Similar comments about the trailing digits apply here as in A173185.
a(n) gives the position of the last element of row n in irregular tables like A238280.
From a(2)=3 onward all terms are divisible by three.
a(n) is divisible by 73 for n >= 72. Therefore a(n)/3 is prime for only 13 values of n: 3, 4, 6, 8, 9, 12, 16, 22, 23, 31, 35, 48 and 53. - Amiram Eldar, Sep 19 2022

Antti Karttunen, Table of n, a(n) for n = 0..250

One less than A173185.

Cf. A003418, A007489, A231722, A236857, A236858.

Prepend[Accumulate @ Table[LCM @@ Range[n], {n, 1, 30}], 0] (* Amiram Eldar, Sep 19 2022 *)

(define (A236856 n) (if (< n 2) n (+ (A236856 (- n 1)) (A003418 n))))

a(n) = A173185(n)-1.

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

Original entry on oeis.org

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

Kival Ngaokrajang, Feb 22 2014

Row n contains A003418(n) terms.

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

			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

Antti Karttunen, Rows 1..10 of the table, flattened
Kival Ngaokrajang, Illustration for n = 1..10

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

(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

cp's OEIS Frontend

A236856 Partial sums of A003418 starting summing from A003418(1), with a(0) = 0.

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