A286146 Lower triangular region of square array A286101.

1, 2, 5, 4, 16, 13, 7, 12, 67, 25, 11, 46, 106, 191, 41, 16, 23, 31, 80, 436, 61, 22, 92, 211, 379, 596, 862, 85, 29, 38, 277, 59, 781, 302, 1541, 113, 37, 154, 58, 631, 991, 193, 1954, 2557, 145, 46, 57, 436, 212, 96, 467, 2416, 822, 4006, 181, 56, 232, 529, 947, 1486, 2146, 2927, 3829, 4852, 5996, 221, 67, 80, 94, 109, 1771, 142, 3487, 355, 706, 1832, 8647

Offset

1,2

Links

Antti Karttunen, Table of n, a(n) for n = 1..10585; the first 145 rows of triangle

Formula

As a triangle (with n >= 1, 1 <= k <= n):

T(n,k) = (1/2)*(2 + ((gcd(n,k)+lcm(n,k))^2) - gcd(n,k) - 3*lcm(n,k)).

Example

The first twelve rows of the triangle:
   1,
   2,   5,
   4,  16,  13,
   7,  12,  67,  25,
  11,  46, 106, 191,   41,
  16,  23,  31,  80,  436,   61,
  22,  92, 211, 379,  596,  862,   85,
  29,  38, 277,  59,  781,  302, 1541,  113,
  37, 154,  58, 631,  991,  193, 1954, 2557,  145,
  46,  57, 436, 212,   96,  467, 2416,  822, 4006,  181,
  56, 232, 529, 947, 1486, 2146, 2927, 3829, 4852, 5996,  221,
  67,  80,  94, 109, 1771,  142, 3487,  355,  706, 1832, 8647, 265
  ----------------------------------------------------------------
For T(4,3) we have gcd(4,3) = 1 and lcm(4,3) = 12, thus T(4,3) = (1/2)*(2 + (12+1)^2 - 1 - 3*12) = 67.
For T(6,4) we have gcd(6,4) = 2 and lcm(6,4) = 12, thus T(6,4) = (1/2)*(2 + (12+2)^2 - 2 - 3*12) = 80.
For T(12,1) we have gcd(12,1) = 1 and lcm(12,1) = 12, thus T(12,1) = T(4,3) = 67.
For T(12,2) we have gcd(12,2) = 2 and lcm(12,1) = 12, thus T(12,1) = T(6,4) = 80.
For T(12,8) we have gcd(12,8) = 4 and lcm(12,8) = 24, thus T(12,8) = (1/2)*(2 + (24+4)^2 - 4 - 3*24) = 355.

Prog

(Scheme) (define (A286146 n) (A286101bi (A002024 n) (A002260 n))) ;; For A286101bi see A286101.
(Python)
from sympy import lcm, gcd
def t(n, k): return (2 + ((gcd(n, k) + lcm(n, k))**2) - gcd(n, k) - 3*lcm(n, k))/2
for n in range(1, 21): print [t(n, k) for k in range(1, n + 1)] # Indranil Ghosh, May 11 2017

Crossrefs

Cf. A286101.

Cf. A286148 (same triangle reversed).

Cf. A000124 (the left edge), A001844 (the right edge).

Sequence in context: A251554 A002518 A093727 * A281922 A065160 A255544

Adjacent sequences: A286143 A286144 A286145 * A286147 A286148 A286149

Keyword

nonn,tabl

Author

Antti Karttunen, May 06 2017

Status

approved