This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A286245 Triangular table T(n,k) = P(A046523(k), floor(n/k)), read by rows as T(1,1), T(2,1), T(2,2), etc. Here P is sequence A000027 used as a pairing function N x N -> N. 4
 1, 2, 3, 4, 3, 3, 7, 5, 3, 10, 11, 5, 3, 10, 3, 16, 8, 5, 10, 3, 21, 22, 8, 5, 10, 3, 21, 3, 29, 12, 5, 14, 3, 21, 3, 36, 37, 12, 8, 14, 3, 21, 3, 36, 10, 46, 17, 8, 14, 5, 21, 3, 36, 10, 21, 56, 17, 8, 14, 5, 21, 3, 36, 10, 21, 3, 67, 23, 12, 19, 5, 27, 3, 36, 10, 21, 3, 78, 79, 23, 12, 19, 5, 27, 3, 36, 10, 21, 3, 78, 3 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Equally: square array A(n,k) = P(A046523(n), floor((n+k-1)/n)), read by descending antidiagonals as A(1,1), A(1,2), A(2,1), etc. Here P is a two-argument form of sequence A000027 used as a pairing function N x N -> N. LINKS Eric Weisstein's World of Mathematics, Pairing Function FORMULA As a triangle (with n >= 1, 1 <= k <= n): T(n,k) = (1/2)*(2 + ((A046523(k)+floor(n/k))^2) - A046523(k) - 3*floor(n/k)). EXAMPLE The first fifteen rows of triangle:     1,     2,  3,     4,  3,  3,     7,  5,  3, 10,    11,  5,  3, 10, 3,    16,  8,  5, 10, 3, 21,    22,  8,  5, 10, 3, 21, 3,    29, 12,  5, 14, 3, 21, 3, 36,    37, 12,  8, 14, 3, 21, 3, 36, 10,    46, 17,  8, 14, 5, 21, 3, 36, 10, 21,    56, 17,  8, 14, 5, 21, 3, 36, 10, 21, 3,    67, 23, 12, 19, 5, 27, 3, 36, 10, 21, 3, 78,    79, 23, 12, 19, 5, 27, 3, 36, 10, 21, 3, 78, 3,    92, 30, 12, 19, 5, 27, 5, 36, 10, 21, 3, 78, 3, 21,   106, 30, 17, 19, 8, 27, 5, 36, 10, 21, 3, 78, 3, 21, 21 PROG (Scheme) (define (A286245 n) (A286245bi (A002260 n) (A004736 n))) (define (A286245bi row col) (let ((a (A046523 row)) (b (quotient (+ row col -1) row))) (* (/ 1 2) (+ (expt (+ a b) 2) (- a) (- (* 3 b)) 2)))) (Python) from sympy import factorint def T(n, m): return ((n + m)**2 - n - 3*m + 2)/2 def P(n):     f = factorint(n)     return sorted([f[i] for i in f]) def a046523(n):     x=1     while True:         if P(n) == P(x): return x         else: x+=1 def t(n, k): return T(a046523(k), int(n/k)) for n in xrange(1, 21): print [t(n, k) for k in xrange(1, n + 1)] # Indranil Ghosh, May 09 2017 CROSSREFS Transpose: A286244. Cf. A000027, A046523, A286156. Cf. A286247 (same triangle but with zeros in positions where k does not divide n), A286235. Sequence in context: A017839 A242294 A234347 * A279849 A106826 A259582 Adjacent sequences:  A286242 A286243 A286244 * A286246 A286247 A286248 KEYWORD nonn,tabl AUTHOR Antti Karttunen, May 06 2017 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
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified June 26 10:45 EDT 2019. Contains 324375 sequences. (Running on oeis4.)