The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A339492 T(n, k) = tau(k) + floor(n/k) - 1, where tau = A000005. Triangle read by rows. 3
 1, 2, 2, 3, 2, 2, 4, 3, 2, 3, 5, 3, 2, 3, 2, 6, 4, 3, 3, 2, 4, 7, 4, 3, 3, 2, 4, 2, 8, 5, 3, 4, 2, 4, 2, 4, 9, 5, 4, 4, 2, 4, 2, 4, 3, 10, 6, 4, 4, 3, 4, 2, 4, 3, 4, 11, 6, 4, 4, 3, 4, 2, 4, 3, 4, 2, 12, 7, 5, 5, 3, 5, 2, 4, 3, 4, 2, 6, 13, 7, 5, 5, 3, 5, 2, 4, 3, 4, 2, 6, 2 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS A simple path in the divisor graph of {1,...,n} is a sequence of distinct numbers between 1 and n such that if m immediately follows k, then either m divides k or k divides m. Let S(n, k) = divisors(k) union {k*j : j = 2..floor(n/k)}. A path p is only valid if the elements of the path p(k-1) are in S(n, p(k)), for k = 2..n. LINKS FORMULA T(n, k) = card(divisors(k) union {k*j : j = 2..floor(n/k)}). EXAMPLE Row 6 lists the cardinalities of the sets {1, 2, 3, 4, 5, 6}, {1, 2, 4, 6}, {1, 3, 6}, {1, 2, 4}, {1, 5}, {1, 2, 3, 6}. The triangle starts: [1]                       1; [2]                      2, 2; [3]                    3, 2, 2; [4]                   4, 3, 2, 3; [5]                 5, 3, 2, 3, 2; [6]                6, 4, 3, 3, 2, 4; [7]              7, 4, 3, 3, 2, 4, 2; [8]             8, 5, 3, 4, 2, 4, 2, 4; [9]           9, 5, 4, 4, 2, 4, 2, 4, 3; [10]        10, 6, 4, 4, 3, 4, 2, 4, 3, 4. MAPLE T := (n, k) -> NumberTheory:-tau(k) + iquo(n, k) - 1: seq(seq(T(n, k), k = 1..n), n = 1..13); CROSSREFS T(n, 1) = A000027(n), T(n, n) = A000005(n), T(2n, n) = A334954(n). Cf. A339491, A339496, A339489. Sequence in context: A230296 A278317 A086454 * A069360 A175509 A213023 Adjacent sequences:  A339489 A339490 A339491 * A339493 A339494 A339495 KEYWORD nonn,tabl AUTHOR Peter Luschny, Dec 31 2020 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 May 8 13:26 EDT 2021. Contains 343666 sequences. (Running on oeis4.)